LMFDB - Embedded newform 87.2.k.a.11.2

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [87,2,Mod(2,87)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("87.2"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(87, base_ring=CyclotomicField(28)) chi = DirichletCharacter(H, H._module([14, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 87 = 3 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	87.k (of order $28$, degree $12$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$0.694698497585$
Analytic rank:	$0$
Dimension:	$96$
Relative dimension:	$8$ over $\Q(\zeta_{28})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{28}]$

Embedding invariants

Embedding label			11.2
Character	$\chi$	$=$	87.11
Dual form			87.2.k.a.8.2

$q$-expansion

comment:q-expansion

sage:f.q_expansion() # note that sage often uses an isomorphic number field

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.576259 - 1.64685i) q^{2} +(0.598445 + 1.62538i) q^{3} +(-0.816387 + 0.651047i) q^{4} +(1.59790 + 0.769508i) q^{5} +(2.33190 - 1.92219i) q^{6} +(1.54710 - 1.94000i) q^{7} +(-1.41204 - 0.887242i) q^{8} +(-2.28373 + 1.94540i) q^{9} +(0.346463 - 3.07494i) q^{10} +(-1.02572 + 0.644501i) q^{11} +(-1.54676 - 0.937325i) q^{12} +(-1.08029 - 0.246570i) q^{13} +(-4.08643 - 1.42990i) q^{14} +(-0.294489 + 3.05770i) q^{15} +(-1.11217 + 4.87274i) q^{16} +(-2.39140 - 2.39140i) q^{17} +(4.51981 + 2.63991i) q^{18} +(0.482698 + 0.0543871i) q^{19} +(-1.80549 + 0.412091i) q^{20} +(4.07910 + 1.35364i) q^{21} +(1.65248 + 1.31781i) q^{22} +(3.99989 + 8.30586i) q^{23} +(0.597080 - 2.82606i) q^{24} +(-1.15631 - 1.44997i) q^{25} +(0.216464 + 1.92117i) q^{26} +(-4.52870 - 2.54771i) q^{27} +2.59103i q^{28} +(-5.27938 - 1.06215i) q^{29} +(5.20529 - 1.27705i) q^{30} +(-9.19909 + 3.21890i) q^{31} +(5.35125 - 0.602941i) q^{32} +(-1.66139 - 1.28148i) q^{33} +(-2.56022 + 5.31635i) q^{34} +(3.96496 - 1.90942i) q^{35} +(0.597858 - 3.07502i) q^{36} +(4.30274 - 6.84777i) q^{37} +(-0.188592 - 0.826274i) q^{38} +(-0.245726 - 1.90345i) q^{39} +(-1.57355 - 2.50430i) q^{40} +(6.28241 - 6.28241i) q^{41} +(-0.121364 - 7.49772i) q^{42} +(-1.18857 + 3.39673i) q^{43} +(0.417782 - 1.19395i) q^{44} +(-5.14617 + 1.35121i) q^{45} +(11.3736 - 11.3736i) q^{46} +(2.28637 + 3.63873i) q^{47} +(-8.58562 + 1.10836i) q^{48} +(0.187557 + 0.821739i) q^{49} +(-1.72155 + 2.73983i) q^{50} +(2.45581 - 5.31805i) q^{51} +(1.04247 - 0.502026i) q^{52} +(5.08537 - 10.5599i) q^{53} +(-1.58600 + 8.92625i) q^{54} +(-2.13494 + 0.240550i) q^{55} +(-3.90581 + 1.36670i) q^{56} +(0.200469 + 0.817117i) q^{57} +(1.29308 + 9.30643i) q^{58} -2.84288i q^{59} +(-1.75029 - 2.68800i) q^{60} +(0.299240 + 2.65582i) q^{61} +(10.6021 + 13.2946i) q^{62} +(0.240929 + 7.44017i) q^{63} +(0.260480 + 0.540893i) q^{64} +(-1.53646 - 1.22529i) q^{65} +(-1.15302 + 3.47454i) q^{66} +(11.9366 - 2.72445i) q^{67} +(3.50922 + 0.395394i) q^{68} +(-11.1065 + 11.4720i) q^{69} +(-5.42938 - 5.42938i) q^{70} +(-1.90444 + 8.34388i) q^{71} +(4.95075 - 0.720761i) q^{72} +(1.41405 + 0.494798i) q^{73} +(-13.7568 - 3.13989i) q^{74} +(1.66476 - 2.74717i) q^{75} +(-0.429477 + 0.269859i) q^{76} +(-0.336554 + 2.98700i) q^{77} +(-2.99310 + 1.50155i) q^{78} +(1.96273 + 1.23326i) q^{79} +(-5.52674 + 6.93032i) q^{80} +(1.43082 - 8.88554i) q^{81} +(-13.9665 - 6.72591i) q^{82} +(6.97313 - 5.56088i) q^{83} +(-4.21141 + 1.55059i) q^{84} +(-1.98101 - 5.66141i) q^{85} +6.27884 q^{86} +(-1.43302 - 9.21664i) q^{87} +2.02018 q^{88} +(3.09433 + 8.84308i) q^{89} +(5.19077 + 7.69634i) q^{90} +(-2.14967 + 1.71431i) q^{91} +(-8.67297 - 4.17668i) q^{92} +(-10.7371 - 13.0257i) q^{93} +(4.67492 - 5.86216i) q^{94} +(0.729452 + 0.458345i) q^{95} +(4.18244 + 8.33700i) q^{96} +(-0.582251 + 5.16762i) q^{97} +(1.24520 - 0.782413i) q^{98} +(1.08865 - 3.46730i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) $ 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/87\mathbb{Z}\right)^\times$.

$n$	$31$	$59$
$\chi(n)$	$e\left(\frac{25}{28}\right)$	$-1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.576259	−	1.64685i	−0.407476	−	1.16450i	−0.946638	−	0.322299i	$-0.895545\pi$
$2$	−0.576259	−	1.64685i	−0.407476	−	1.16450i	0.539162	−	0.842202i	$-0.318741\pi$
$3$	0.598445	+	1.62538i	0.345512	+	0.938414i
$3$	0.598445	+	1.62538i	0.345512	+	0.938414i
$4$	−0.816387	+	0.651047i	−0.408194	+	0.325524i
$5$	1.59790	+	0.769508i	0.714602	+	0.344134i	0.755608	−	0.655025i	$-0.227342\pi$
$5$	1.59790	+	0.769508i	0.714602	+	0.344134i	−0.0410052	+	0.999159i	$0.513056\pi$
$6$	2.33190	−	1.92219i	0.951996	−	0.784731i
$7$	1.54710	−	1.94000i	0.584749	−	0.733252i	−0.398166	−	0.917313i	$-0.630353\pi$
$7$	1.54710	−	1.94000i	0.584749	−	0.733252i	0.982915	+	0.184062i	$0.0589246\pi$
$8$	−1.41204	−	0.887242i	−0.499231	−	0.313687i
$9$	−2.28373	+	1.94540i	−0.761243	+	0.648467i
$10$	0.346463	−	3.07494i	0.109561	−	0.972382i
$11$	−1.02572	+	0.644501i	−0.309265	+	0.194324i	−0.677717	−	0.735322i	$-0.737031\pi$
$11$	−1.02572	+	0.644501i	−0.309265	+	0.194324i	0.368452	+	0.929647i	$0.379888\pi$
$12$	−1.54676	−	0.937325i	−0.446512	−	0.270582i
$13$	−1.08029	−	0.246570i	−0.299620	−	0.0683863i	0.0700682	−	0.997542i	$-0.477678\pi$
$13$	−1.08029	−	0.246570i	−0.299620	−	0.0683863i	−0.369688	+	0.929156i	$0.620535\pi$
$14$	−4.08643	−	1.42990i	−1.09214	−	0.382158i
$15$	−0.294489	+	3.05770i	−0.0760367	+	0.789496i
$16$	−1.11217	+	4.87274i	−0.278042	+	1.21818i
$17$	−2.39140	−	2.39140i	−0.579999	−	0.579999i	0.354904	−	0.934903i	$-0.384514\pi$
$17$	−2.39140	−	2.39140i	−0.579999	−	0.579999i	−0.934903	+	0.354904i	$0.884514\pi$
$18$	4.51981	+	2.63991i	1.06533	+	0.622232i
$19$	0.482698	+	0.0543871i	0.110739	+	0.0124772i	0.167160	−	0.985930i	$-0.446540\pi$
$19$	0.482698	+	0.0543871i	0.110739	+	0.0124772i	−0.0564212	+	0.998407i	$0.517969\pi$
$20$	−1.80549	+	0.412091i	−0.403720	+	0.0921465i
$21$	4.07910	+	1.35364i	0.890132	+	0.295389i
$22$	1.65248	+	1.31781i	0.352309	+	0.280957i
$23$	3.99989	+	8.30586i	0.834035	+	1.73189i	0.665779	+	0.746149i	$0.268099\pi$
$23$	3.99989	+	8.30586i	0.834035	+	1.73189i	0.168257	+	0.985743i	$0.446186\pi$
$24$	0.597080	−	2.82606i	0.121878	−	0.576868i
$25$	−1.15631	−	1.44997i	−0.231262	−	0.289993i
$26$	0.216464	+	1.92117i	0.0424522	+	0.376773i
$27$	−4.52870	−	2.54771i	−0.871550	−	0.490307i
$28$			2.59103i			0.489658i
$29$	−5.27938	−	1.06215i	−0.980356	−	0.197236i
$29$	−5.27938	−	1.06215i	−0.980356	−	0.197236i
$30$	5.20529	−	1.27705i	0.950352	−	0.233156i
$31$	−9.19909	+	3.21890i	−1.65221	+	0.578132i	−0.985869	−	0.167520i	$-0.946424\pi$
$31$	−9.19909	+	3.21890i	−1.65221	+	0.578132i	−0.666337	+	0.745651i	$0.732139\pi$
$32$	5.35125	−	0.602941i	0.945977	−	0.106586i
$33$	−1.66139	−	1.28148i	−0.289212	−	0.223078i
$34$	−2.56022	+	5.31635i	−0.439074	+	0.911746i
$35$	3.96496	−	1.90942i	0.670200	−	0.322751i
$36$	0.597858	−	3.07502i	0.0996430	−	0.512503i
$37$	4.30274	−	6.84777i	0.707366	−	1.12577i	−0.278855	−	0.960333i	$-0.589955\pi$
$37$	4.30274	−	6.84777i	0.707366	−	1.12577i	0.986221	−	0.165434i	$-0.0529024\pi$
$38$	−0.188592	−	0.826274i	−0.0305936	−	0.134039i
$39$	−0.245726	−	1.90345i	−0.0393477	−	0.304796i
$40$	−1.57355	−	2.50430i	−0.248801	−	0.395964i
$41$	6.28241	−	6.28241i	0.981148	−	0.981148i	−0.0186776	−	0.999826i	$-0.505946\pi$
$41$	6.28241	−	6.28241i	0.981148	−	0.981148i	0.999826	+	0.0186776i	$0.00594559\pi$
$42$	−0.121364	−	7.49772i	−0.0187269	−	1.15692i
$43$	−1.18857	+	3.39673i	−0.181255	+	0.517997i	−0.998281	−	0.0586033i	$-0.981335\pi$
$43$	−1.18857	+	3.39673i	−0.181255	+	0.517997i	0.817026	+	0.576600i	$0.195621\pi$
$44$	0.417782	−	1.19395i	0.0629830	−	0.179995i
$45$	−5.14617	+	1.35121i	−0.767146	+	0.201427i
$46$	11.3736	−	11.3736i	1.67694	−	1.67694i
$47$	2.28637	+	3.63873i	0.333501	+	0.530764i	0.970812	−	0.239843i	$-0.0770960\pi$
$47$	2.28637	+	3.63873i	0.333501	+	0.530764i	−0.637311	+	0.770607i	$0.719953\pi$
$48$	−8.58562	+	1.10836i	−1.23923	+	0.159978i
$49$	0.187557	+	0.821739i	0.0267938	+	0.117391i
$50$	−1.72155	+	2.73983i	−0.243463	+	0.387470i
$51$	2.45581	−	5.31805i	0.343883	−	0.744676i
$52$	1.04247	−	0.502026i	0.144564	−	0.0696185i
$53$	5.08537	−	10.5599i	0.698530	−	1.45051i	−0.185290	−	0.982684i	$-0.559322\pi$
$53$	5.08537	−	10.5599i	0.698530	−	1.45051i	0.883820	−	0.467828i	$-0.154963\pi$
$54$	−1.58600	+	8.92625i	−0.215827	+	1.21471i
$55$	−2.13494	+	0.240550i	−0.287875	+	0.0324358i
$56$	−3.90581	+	1.36670i	−0.521936	+	0.182633i
$57$	0.200469	+	0.817117i	0.0265527	+	0.108230i
$58$	1.29308	+	9.30643i	0.169790	+	1.22199i
$59$		−	2.84288i		−	0.370111i	−0.982728	−	0.185056i	$-0.940754\pi$
$59$		−	2.84288i		−	0.370111i	0.982728	−	0.185056i	$-0.0592465\pi$
$60$	−1.75029	−	2.68800i	−0.225962	−	0.347019i
$61$	0.299240	+	2.65582i	0.0383137	+	0.340043i	0.998216	+	0.0597083i	$0.0190170\pi$
$61$	0.299240	+	2.65582i	0.0383137	+	0.340043i	−0.959902	+	0.280335i	$0.909554\pi$
$62$	10.6021	+	13.2946i	1.34647	+	1.68842i
$63$	0.240929	+	7.44017i	0.0303542	+	0.937373i
$64$	0.260480	+	0.540893i	0.0325600	+	0.0676116i
$65$	−1.53646	−	1.22529i	−0.190575	−	0.151978i
$66$	−1.15302	+	3.47454i	−0.141927	+	0.427686i
$67$	11.9366	−	2.72445i	1.45829	−	0.332844i	0.581430	−	0.813596i	$-0.302493\pi$
$67$	11.9366	−	2.72445i	1.45829	−	0.332844i	0.876857	+	0.480752i	$0.159636\pi$
$68$	3.50922	+	0.395394i	0.425555	+	0.0479486i
$69$	−11.1065	+	11.4720i	−1.33706	+	1.38106i
$70$	−5.42938	−	5.42938i	−0.648935	−	0.648935i
$71$	−1.90444	+	8.34388i	−0.226015	+	0.990236i	0.726839	+	0.686808i	$0.240988\pi$
$71$	−1.90444	+	8.34388i	−0.226015	+	0.990236i	−0.952854	+	0.303428i	$0.901869\pi$
$72$	4.95075	−	0.720761i	0.583451	−	0.0849425i
$73$	1.41405	+	0.494798i	0.165502	+	0.0579118i	0.411758	−	0.911293i	$-0.364915\pi$
$73$	1.41405	+	0.494798i	0.165502	+	0.0579118i	−0.246256	+	0.969205i	$0.579200\pi$
$74$	−13.7568	−	3.13989i	−1.59919	−	0.365005i
$75$	1.66476	−	2.74717i	0.192230	−	0.317215i
$76$	−0.429477	+	0.269859i	−0.0492644	+	0.0309549i
$77$	−0.336554	+	2.98700i	−0.0383539	+	0.340400i
$78$	−2.99310	+	1.50155i	−0.338902	+	0.170018i
$79$	1.96273	+	1.23326i	0.220824	+	0.138753i	0.637901	−	0.770118i	$-0.279803\pi$
$79$	1.96273	+	1.23326i	0.220824	+	0.138753i	−0.417077	+	0.908871i	$0.636946\pi$
$80$	−5.52674	+	6.93032i	−0.617909	+	0.774833i
$81$	1.43082	−	8.88554i	0.158980	−	0.987282i
$82$	−13.9665	−	6.72591i	−1.54234	−	0.742753i
$83$	6.97313	−	5.56088i	0.765400	−	0.610386i	−0.160988	−	0.986956i	$-0.551468\pi$
$83$	6.97313	−	5.56088i	0.765400	−	0.610386i	0.926388	+	0.376570i	$0.122897\pi$
$84$	−4.21141	+	1.55059i	−0.459502	+	0.169183i
$85$	−1.98101	−	5.66141i	−0.214871	−	0.614067i
$86$	6.27884			0.677065
$87$	−1.43302	−	9.21664i	−0.153636	−	0.988128i
$88$	2.02018			0.215352
$89$	3.09433	+	8.84308i	0.327998	+	0.937365i	0.983299	+	0.181997i	$0.0582561\pi$
$89$	3.09433	+	8.84308i	0.327998	+	0.937365i	−0.655301	+	0.755368i	$0.727458\pi$
$90$	5.19077	+	7.69634i	0.547155	+	0.811265i
$91$	−2.14967	+	1.71431i	−0.225347	+	0.179708i
$92$	−8.67297	−	4.17668i	−0.904220	−	0.435449i
$93$	−10.7371	−	13.0257i	−1.11338	−	1.35070i
$94$	4.67492	−	5.86216i	0.482181	−	0.604636i
$95$	0.729452	+	0.458345i	0.0748402	+	0.0470252i
$96$	4.18244	+	8.33700i	0.426868	+	0.850891i
$97$	−0.582251	+	5.16762i	−0.0591186	+	0.524692i	0.928897	+	0.370338i	$0.120758\pi$
$97$	−0.582251	+	5.16762i	−0.0591186	+	0.524692i	−0.988016	+	0.154354i	$0.950670\pi$
$98$	1.24520	−	0.782413i	0.125784	−	0.0790356i
$99$	1.08865	−	3.46730i	0.109413	−	0.348476i
$100$	1.88799	+	0.430922i	0.188799	+	0.0430922i
$101$	−11.4685	−	4.01299i	−1.14116	−	0.399308i	−0.307476	−	0.951556i	$-0.599484\pi$
$101$	−11.4685	−	4.01299i	−1.14116	−	0.399308i	−0.833680	+	0.552248i	$0.813770\pi$
$102$	−10.1732	−	0.979789i	−1.00730	−	0.0970136i
$103$	2.53000	−	11.0847i	0.249288	−	1.09220i	−0.682980	−	0.730437i	$-0.739317\pi$
$103$	2.53000	−	11.0847i	0.249288	−	1.09220i	0.932269	−	0.361767i	$-0.117826\pi$
$104$	1.30665	+	1.30665i	0.128127	+	0.128127i
$105$	5.47635	+	5.30188i	0.534437	+	0.517411i
$106$	−20.3211	−	2.28963i	−1.97376	−	0.222389i
$107$	1.16741	−	0.266455i	0.112858	−	0.0257592i	−0.165719	−	0.986173i	$-0.552994\pi$
$107$	1.16741	−	0.266455i	0.112858	−	0.0257592i	0.278577	+	0.960414i	$0.410137\pi$
$108$	5.35586	−	0.868480i	0.515368	−	0.0835696i
$109$	8.29478	+	6.61487i	0.794496	+	0.633589i	0.934259	−	0.356596i	$-0.116063\pi$
$109$	8.29478	+	6.61487i	0.794496	+	0.633589i	−0.139763	+	0.990185i	$0.544634\pi$
$110$	1.62643	+	3.37731i	0.155074	+	0.322014i
$111$	13.7052	+	2.89558i	1.30084	+	0.274836i
$112$	7.73248	+	9.69622i	0.730651	+	0.916207i
$113$	−0.516504	−	4.58410i	−0.0485886	−	0.431236i	−0.994332	−	0.106321i	$-0.966093\pi$
$113$	−0.516504	−	4.58410i	−0.0485886	−	0.431236i	0.945743	−	0.324915i	$-0.105336\pi$
$114$	1.23015	−	0.801013i	0.115214	−	0.0750217i
$115$			16.3499i			1.52463i
$116$	5.00153	−	2.57000i	0.464380	−	0.238618i
$117$	2.94678	−	1.53851i	0.272430	−	0.142235i
$118$	−4.68180	+	1.63823i	−0.430995	+	0.150812i
$119$	−8.33905	+	0.939585i	−0.764440	+	0.0861316i
$120$	3.12875	−	4.05631i	0.285615	−	0.370289i
$121$	−4.13601	+	8.58851i	−0.376001	+	0.780773i
$122$	4.20131	−	2.02325i	0.380369	−	0.183176i
$123$	13.9710	+	6.45164i	1.25972	+	0.581725i
$124$	5.41436	−	8.61691i	0.486224	−	0.773821i
$125$	−2.70515	−	11.8520i	−0.241956	−	1.06008i
$126$	12.1140	−	4.68424i	1.07920	−	0.417305i
$127$	1.38905	+	2.21065i	0.123258	+	0.196164i	0.902653	−	0.430369i	$-0.141616\pi$
$127$	1.38905	+	2.21065i	0.123258	+	0.196164i	−0.779395	+	0.626532i	$0.784474\pi$
$128$	8.35637	−	8.35637i	0.738605	−	0.738605i
$129$	−6.23228	+	0.100881i	−0.548722	+	0.00888206i
$130$	−1.13247	+	3.23641i	−0.0993242	+	0.283852i
$131$	−0.142233	+	0.406478i	−0.0124269	+	0.0355142i	−0.949930	−	0.312464i	$-0.898846\pi$
$131$	−0.142233	+	0.406478i	−0.0124269	+	0.0355142i	0.937503	+	0.347978i	$0.113132\pi$
$132$	2.19065	−	0.0354596i	0.190671	−	0.00308636i
$133$	0.852294	−	0.852294i	0.0739033	−	0.0739033i
$134$	−11.3653	−	18.0878i	−0.981815	−	1.56255i
$135$	−5.27593	−	7.55586i	−0.454080	−	0.650305i
$136$	1.25499	+	5.49849i	0.107615	+	0.471492i
$137$	−2.75997	+	4.39247i	−0.235800	+	0.375274i	−0.943572	−	0.331167i	$-0.892558\pi$
$137$	−2.75997	+	4.39247i	−0.235800	+	0.375274i	0.707772	+	0.706441i	$0.249701\pi$
$138$	25.2928	+	11.6799i	2.15307	+	0.994261i
$139$	−5.43195	+	2.61589i	−0.460732	+	0.221877i	−0.649827	−	0.760082i	$-0.725159\pi$
$139$	−5.43195	+	2.61589i	−0.460732	+	0.221877i	0.189095	+	0.981959i	$0.439445\pi$
$140$	−1.99382	+	4.14020i	−0.168508	+	0.349911i
$141$	−4.54606	+	5.89380i	−0.382848	+	0.496348i
$142$	14.8386	−	1.67191i	1.24523	−	0.140303i
$143$	1.26699	−	0.443339i	0.105951	−	0.0370739i
$144$	−6.93953	−	13.2916i	−0.578295	−	1.10763i
$145$	−7.61858	−	5.75973i	−0.632689	−	0.478320i
$146$		−	2.61387i		−	0.216325i
$147$	−1.22340	+	0.796617i	−0.100904	+	0.0657038i
$148$	0.945520	+	8.39172i	0.0777213	+	0.689795i
$149$	−2.74781	−	3.44564i	−0.225109	−	0.282278i	0.656432	−	0.754385i	$-0.272065\pi$
$149$	−2.74781	−	3.44564i	−0.225109	−	0.282278i	−0.881541	+	0.472107i	$0.843493\pi$
$150$	−5.48351	−	1.15853i	−0.447727	−	0.0945940i
$151$	−3.83234	−	7.95793i	−0.311871	−	0.647607i	0.684836	−	0.728698i	$-0.259874\pi$
$151$	−3.83234	−	7.95793i	−0.311871	−	0.647607i	−0.996707	+	0.0810904i	$0.974160\pi$
$152$	−0.633334	−	0.505067i	−0.0513701	−	0.0409663i
$153$	10.1135	+	0.809072i	0.817631	+	0.0654096i
$154$	5.11309	−	1.16703i	0.412025	−	0.0940420i
$155$	−17.1762	−	1.93529i	−1.37962	−	0.155446i
$156$	1.43984	+	1.39397i	0.115280	+	0.111607i
$157$	−7.17901	−	7.17901i	−0.572948	−	0.572948i	0.360003	−	0.932951i	$-0.382776\pi$
$157$	−7.17901	−	7.17901i	−0.572948	−	0.572948i	−0.932951	+	0.360003i	$0.882776\pi$
$158$	0.899964	−	3.94300i	0.0715973	−	0.313688i
$159$	20.2072	+	1.94616i	1.60253	+	0.154341i
$160$	9.01473	+	3.15439i	0.712677	+	0.249377i
$161$	22.3016	+	5.09020i	1.75761	+	0.401164i
$162$	−15.4577	+	2.76401i	−1.21447	+	0.217161i
$163$	−3.44823	+	2.16667i	−0.270086	+	0.169706i	−0.660265	−	0.751033i	$-0.729556\pi$
$163$	−3.44823	+	2.16667i	−0.270086	+	0.169706i	0.390179	+	0.920739i	$0.372413\pi$
$164$	−1.03874	+	9.21903i	−0.0811116	+	0.719885i
$165$	−1.66863	−	3.32614i	−0.129903	−	0.258939i
$166$	−13.1763	−	8.27920i	−1.02268	−	0.642591i
$167$	−12.6392	+	15.8490i	−0.978047	+	1.22643i	−0.00402168	+	0.999992i	$0.501280\pi$
$167$	−12.6392	+	15.8490i	−0.978047	+	1.22643i	−0.974025	+	0.226440i	$0.927291\pi$
$168$	−4.55883	−	5.53054i	−0.351721	−	0.426690i
$169$	−10.6064	−	5.10775i	−0.815874	−	0.392904i
$170$	−8.18194	+	6.52488i	−0.627526	+	0.500435i
$171$	−1.20816	+	0.814837i	−0.0923900	+	0.0623122i
$172$	−1.24110	−	3.54686i	−0.0946331	−	0.270446i
$173$	−3.30578			−0.251334			−0.125667	−	0.992072i	$-0.540107\pi$
$173$	−3.30578			−0.251334			−0.125667	+	0.992072i	$0.540107\pi$
$174$	−14.3527	+	7.67114i	−1.08807	+	0.581548i
$175$	−4.60186			−0.347868
$176$	−1.99971	−	5.71484i	−0.150734	−	0.430772i
$177$	4.62076	−	1.70130i	0.347317	−	0.127878i
$178$	12.7801	−	10.1918i	0.957910	−	0.763908i
$179$	4.99423	+	2.40509i	0.373286	+	0.179765i	0.611115	−	0.791542i	$-0.290721\pi$
$179$	4.99423	+	2.40509i	0.373286	+	0.179765i	−0.237829	+	0.971307i	$0.576436\pi$
$180$	3.32157	−	4.45351i	0.247575	−	0.331945i
$181$	−4.91454	+	6.16264i	−0.365295	+	0.458065i	−0.930180	−	0.367105i	$-0.880349\pi$
$181$	−4.91454	+	6.16264i	−0.365295	+	0.458065i	0.564885	+	0.825170i	$0.308921\pi$
$182$	4.06197	+	2.55231i	0.301094	+	0.189190i
$183$	−4.13765	+	2.07574i	−0.305864	+	0.153443i
$184$	1.72131	−	15.2771i	0.126897	−	1.12624i
$185$	12.1448	−	7.63106i	0.892901	−	0.561047i
$186$	−15.2641	+	25.1886i	−1.11922	+	1.84692i
$187$	3.99416	+	0.911640i	0.292082	+	0.0666657i
$188$	−4.23555	−	1.48208i	−0.308909	−	0.108092i
$189$	−11.9489	+	4.84413i	−0.869157	+	0.352359i
$190$	0.334474	−	1.46543i	0.0242653	−	0.106313i
$191$	6.59651	+	6.59651i	0.477307	+	0.477307i	0.904269	−	0.426963i	$-0.140416\pi$
$191$	6.59651	+	6.59651i	0.477307	+	0.477307i	−0.426963	+	0.904269i	$0.640416\pi$
$192$	−0.723274	+	0.747074i	−0.0521978	+	0.0539154i
$193$	11.7855	+	1.32791i	0.848338	+	0.0955847i	0.525421	−	0.850843i	$-0.323908\pi$
$193$	11.7855	+	1.32791i	0.848338	+	0.0955847i	0.322917	+	0.946427i	$0.395337\pi$
$194$	8.84584	−	2.01900i	0.635094	−	0.144956i
$195$	1.07207	−	3.23061i	0.0767728	−	0.231349i
$196$	−0.688110	−	0.548749i	−0.0491507	−	0.0391964i
$197$	1.76954	+	3.67449i	0.126075	+	0.261797i	0.954447	−	0.298382i	$-0.0964468\pi$
$197$	1.76954	+	3.67449i	0.126075	+	0.261797i	−0.828372	+	0.560179i	$0.810733\pi$
$198$	−6.33747	+	0.205221i	−0.450384	+	0.0145844i
$199$	6.84164	+	8.57915i	0.484991	+	0.608160i	0.962770	−	0.270320i	$-0.0871296\pi$
$199$	6.84164	+	8.57915i	0.484991	+	0.608160i	−0.477779	+	0.878480i	$0.658558\pi$
$200$	0.346281	+	3.07333i	0.0244858	+	0.217317i
$201$	11.5717	+	17.7711i	0.816202	+	1.25348i
$202$			21.1994i			1.49159i
$203$	−10.2283	+	8.59875i	−0.717886	+	0.603514i
$204$	1.45741	+	5.94044i	0.102039	+	0.415914i
$205$	14.8730	−	5.20430i	1.03878	−	0.363484i
$206$	−19.7127	+	2.22109i	−1.37345	+	0.154751i
$207$	−25.2929	−	11.1869i	−1.75798	−	0.777545i
$208$	2.40294	−	4.98976i	0.166614	−	0.345978i
$209$	−0.530165	+	0.255314i	−0.0366722	+	0.0176604i
$210$	5.57563	−	12.0740i	0.384755	−	0.833185i
$211$	13.1840	−	20.9822i	0.907622	−	1.44447i	0.0118637	−	0.999930i	$-0.496224\pi$
$211$	13.1840	−	20.9822i	0.907622	−	1.44447i	0.895758	−	0.444542i	$-0.146634\pi$
$212$	2.72335	+	11.9318i	0.187040	+	0.819478i
$213$	−14.7017	+	1.89792i	−1.00734	+	0.130043i
$214$	−1.11154	−	1.76901i	−0.0759836	−	0.120927i
$215$	−4.51303	+	4.51303i	−0.307786	+	0.307786i
$216$	4.13426	+	7.61552i	0.281301	+	0.518170i
$217$	−7.98724	+	22.8262i	−0.542209	+	1.54954i
$218$	6.11377	−	17.4722i	0.414077	−	1.18336i
$219$	0.0419965	+	2.59448i	0.00283786	+	0.175319i
$220$	1.58633	−	1.58633i	0.106950	−	0.106950i
$221$	1.99377	+	3.17306i	0.134115	+	0.213443i
$222$	−3.12914	−	24.2390i	−0.210014	−	1.62682i
$223$	−4.07939	−	17.8730i	−0.273176	−	1.19686i	−0.906240	−	0.422764i	$-0.861060\pi$
$223$	−4.07939	−	17.8730i	−0.273176	−	1.19686i	0.633063	−	0.774100i	$-0.281797\pi$
$224$	7.10922	−	11.3143i	0.475005	−	0.755965i
$225$	5.46146	+	1.06184i	0.364097	+	0.0707894i
$226$	−7.25170	+	3.49224i	−0.482376	+	0.232300i
$227$	−10.5337	+	21.8734i	−0.699145	+	1.45179i	0.184115	+	0.982905i	$0.441058\pi$
$227$	−10.5337	+	21.8734i	−0.699145	+	1.45179i	−0.883259	+	0.468884i	$0.844656\pi$
$228$	−0.695642	−	0.536569i	−0.0460700	−	0.0355352i
$229$	−6.13894	+	0.691693i	−0.405673	+	0.0457084i	−0.312444	−	0.949936i	$-0.601148\pi$
$229$	−6.13894	+	0.691693i	−0.405673	+	0.0457084i	−0.0932293	+	0.995645i	$0.529719\pi$
$230$	26.9259	−	9.42176i	1.77544	−	0.621253i
$231$	−5.05642	+	1.24053i	−0.332688	+	0.0816206i
$232$	6.51229	+	6.18388i	0.427553	+	0.405992i
$233$			13.5660i			0.888735i	0.895845	+	0.444368i	$0.146572\pi$
$233$			13.5660i			0.888735i	−0.895845	+	0.444368i	$0.853428\pi$
$234$	−4.23180	−	3.96633i	−0.276642	−	0.259287i
$235$	0.853352	+	7.57371i	0.0556666	+	0.494054i
$236$	1.85085	+	2.32089i	0.120480	+	0.151077i
$237$	−0.829938	+	3.92822i	−0.0539103	+	0.255165i
$238$	6.35281	+	13.1917i	0.411792	+	0.855094i
$239$	−13.4160	−	10.6989i	−0.867808	−	0.692053i	0.0847532	−	0.996402i	$-0.472990\pi$
$239$	−13.4160	−	10.6989i	−0.867808	−	0.692053i	−0.952561	+	0.304349i	$0.901561\pi$
$240$	−14.5719	−	4.83565i	−0.940609	−	0.312140i
$241$	15.9674	−	3.64445i	1.02855	−	0.234760i	0.325231	−	0.945634i	$-0.394558\pi$
$241$	15.9674	−	3.64445i	1.02855	−	0.234760i	0.703319	+	0.710875i	$0.251701\pi$
$242$	16.5274	+	1.86219i	1.06242	+	0.119706i
$243$	15.2987	−	2.99187i	0.981409	−	0.191929i
$244$	−1.97336	−	1.97336i	−0.126332	−	0.126332i
$245$	−0.332638	+	1.45738i	−0.0212515	+	0.0931088i
$246$	2.57399	−	26.7260i	0.164112	−	1.70399i
$247$	−0.508046	−	0.177773i	−0.0323262	−	0.0113114i
$248$	15.8454	+	3.61661i	1.00618	+	0.229655i
$249$	13.2116	+	8.00611i	0.837250	+	0.507366i
$250$	−17.9597	+	11.2848i	−1.13587	+	0.713714i
$251$	2.30792	−	20.4833i	0.145675	−	1.29290i	−0.681860	−	0.731483i	$-0.738829\pi$
$251$	2.30792	−	20.4833i	0.145675	−	1.29290i	0.827535	−	0.561415i	$-0.189743\pi$
$252$	−5.04059	−	5.91720i	−0.317527	−	0.372749i
$253$	−9.45589	−	5.94153i	−0.594487	−	0.373541i
$254$	2.84017	−	3.56146i	0.178208	−	0.223466i
$255$	8.01643	−	6.60795i	0.502008	−	0.413806i
$256$	−17.4954	−	8.42532i	−1.09346	−	0.526582i
$257$	11.3696	−	9.06698i	0.709218	−	0.565582i	−0.201061	−	0.979579i	$-0.564439\pi$
$257$	11.3696	−	9.06698i	0.709218	−	0.565582i	0.910279	+	0.413996i	$0.135867\pi$
$258$	3.75754	+	10.2055i	0.233934	+	0.635368i
$259$	−6.62792	−	18.9415i	−0.411839	−	1.17697i
$260$	2.05207			0.127264
$261$	14.1230	−	7.84485i	0.874190	−	0.485584i
$262$	0.751373			0.0464200
$263$	−3.08537	−	8.81747i	−0.190252	−	0.543709i	0.808761	−	0.588138i	$-0.200139\pi$
$263$	−3.08537	−	8.81747i	−0.190252	−	0.543709i	−0.999013	+	0.0444293i	$0.985853\pi$
$264$	1.20897	+	3.28356i	0.0744067	+	0.202089i
$265$	16.2518	−	12.9604i	0.998342	−	0.796151i
$266$	−1.89474	−	0.912461i	−0.116174	−	0.0559466i
$267$	−12.5216	+	10.3216i	−0.766309	+	0.631669i
$268$	−7.97114	+	9.99549i	−0.486915	+	0.610572i
$269$	4.66339	+	2.93020i	0.284332	+	0.178657i	0.666645	−	0.745375i	$-0.267730\pi$
$269$	4.66339	+	2.93020i	0.284332	+	0.178657i	−0.382313	+	0.924033i	$0.624873\pi$
$270$	−9.40309	+	13.0428i	−0.572254	+	0.793760i
$271$	−2.43068	+	21.5728i	−0.147653	+	1.31046i	0.673261	+	0.739405i	$0.264893\pi$
$271$	−2.43068	+	21.5728i	−0.147653	+	1.31046i	−0.820914	+	0.571052i	$0.806536\pi$
$272$	14.3123	−	8.99301i	0.867810	−	0.545281i
$273$	−4.07286	−	2.46812i	−0.246501	−	0.149377i
$274$	8.82421	+	2.01407i	0.533090	+	0.121674i
$275$	2.12055	+	0.742012i	0.127874	+	0.0447450i
$276$	1.59841	−	16.5964i	0.0962128	−	0.998986i
$277$	−5.43368	+	23.8065i	−0.326478	+	1.43040i	0.499314	+	0.866421i	$0.333585\pi$
$277$	−5.43368	+	23.8065i	−0.326478	+	1.43040i	−0.825792	+	0.563974i	$0.809272\pi$
$278$	7.43820	+	7.43820i	0.446113	+	0.446113i
$279$	14.7462	−	25.2470i	0.882829	−	1.51150i
$280$	−7.29279	−	0.821700i	−0.435827	−	0.0491060i
$281$	22.3808	−	5.10828i	1.33513	−	0.304734i	0.505392	−	0.862890i	$-0.331348\pi$
$281$	22.3808	−	5.10828i	1.33513	−	0.304734i	0.829737	+	0.558155i	$0.188491\pi$
$282$	12.3259	+	4.09035i	0.733999	+	0.243577i
$283$	−20.7543	−	16.5510i	−1.23372	−	0.983857i	−0.999933	−	0.0115684i	$-0.996318\pi$
$283$	−20.7543	−	16.5510i	−1.23372	−	0.983857i	−0.233784	−	0.972288i	$-0.575111\pi$
$284$	−3.87750	−	8.05171i	−0.230087	−	0.477781i
$285$	−0.308449	+	1.45993i	−0.0182709	+	0.0864789i
$286$	−1.46023	−	1.83107i	−0.0863452	−	0.108273i
$287$	−2.46837	−	21.9074i	−0.145703	−	1.29315i
$288$	−11.0478	+	11.7873i	−0.651000	+	0.694573i
$289$		−	5.56243i		−	0.327202i
$290$	−5.09516	+	15.8658i	−0.299198	+	0.931671i
$291$	−8.74780	+	2.14616i	−0.512805	+	0.125810i
$292$	−1.47655	+	0.516668i	−0.0864086	+	0.0302357i
$293$	−18.8457	+	2.12340i	−1.10098	+	0.124051i	−0.643704	−	0.765275i	$-0.722603\pi$
$293$	−18.8457	+	2.12340i	−1.10098	+	0.124051i	−0.457275	+	0.889325i	$0.651174\pi$
$294$	2.01690	+	1.55570i	0.117628	+	0.0907302i
$295$	2.18762	−	4.54263i	0.127368	−	0.264482i
$296$	−12.1513	+	5.85174i	−0.706278	+	0.340125i
$297$	6.28717	−	0.305522i	0.364819	−	0.0177282i
$298$	−4.09101	+	6.51081i	−0.236986	+	0.377161i
$299$	−2.27308	−	9.95903i	−0.131456	−	0.575946i
$300$	0.429447	+	3.32659i	0.0247941	+	0.192061i
$301$	4.75084	+	7.56091i	0.273834	+	0.435804i
$302$	−10.8971	+	10.8971i	−0.627059	+	0.627059i
$303$	−0.340607	−	21.0422i	−0.0195673	−	1.20884i
$304$	−0.801856	+	2.29157i	−0.0459896	+	0.131431i
$305$	−1.56552	+	4.47401i	−0.0896416	+	0.256181i
$306$	−4.49559	−	17.1217i	−0.256996	−	0.978784i
$307$	1.83383	−	1.83383i	0.104662	−	0.104662i	−0.652837	−	0.757499i	$-0.726421\pi$
$307$	1.83383	−	1.83383i	0.104662	−	0.104662i	0.757499	+	0.652837i	$0.226421\pi$
$308$	−1.66992	−	2.65766i	−0.0951525	−	0.151434i
$309$	19.5308	−	2.52134i	1.11107	−	0.143434i
$310$	6.71079	+	29.4019i	0.381147	+	1.66991i
$311$	−10.6017	+	16.8725i	−0.601166	+	0.956750i	0.398058	+	0.917360i	$0.369684\pi$
$311$	−10.6017	+	16.8725i	−0.601166	+	0.956750i	−0.999224	+	0.0393897i	$0.987459\pi$
$312$	−1.34184	+	2.90576i	−0.0759670	+	0.164506i
$313$	10.9283	−	5.26280i	0.617705	−	0.297471i	−0.0987415	−	0.995113i	$-0.531482\pi$
$313$	10.9283	−	5.26280i	0.617705	−	0.297471i	0.716446	+	0.697642i	$0.245767\pi$
$314$	−7.68581	+	15.9597i	−0.433735	+	0.900661i
$315$	−5.34029	+	12.0740i	−0.300891	+	0.680295i
$316$	−2.40526	+	0.271007i	−0.135306	+	0.0152454i
$317$	−19.6625	+	6.88021i	−1.10436	+	0.386431i	−0.820044	−	0.572301i	$-0.806051\pi$
$317$	−19.6625	+	6.88021i	−1.10436	+	0.386431i	−0.284312	+	0.958732i	$0.591765\pi$
$318$	−8.43951	−	34.3997i	−0.473264	−	1.92904i
$319$	6.09970	−	2.31310i	0.341518	−	0.129509i
$320$			1.06473i			0.0595204i
$321$	1.13172	+	1.73804i	0.0631667	+	0.0970077i
$322$	−4.46870	−	39.6608i	−0.249031	−	2.21021i
$323$	−1.02426	−	1.28439i	−0.0569915	−	0.0714651i
$324$	4.61680	+	8.18557i	0.256489	+	0.454754i
$325$	0.891636	+	1.85150i	0.0494590	+	0.102703i
$326$	5.55525	+	4.43016i	0.307677	+	0.245364i
$327$	−5.78771	+	17.4408i	−0.320061	+	0.964479i
$328$	−14.4450	+	3.29698i	−0.797593	+	0.182045i
$329$	10.5964	+	1.19393i	0.584198	+	0.0658233i
$330$	−4.51610	+	4.66470i	−0.248603	+	0.256783i
$331$	12.4740	+	12.4740i	0.685633	+	0.685633i	0.961264	−	0.275630i	$-0.0888866\pi$
$331$	12.4740	+	12.4740i	0.685633	+	0.685633i	−0.275630	+	0.961264i	$0.588887\pi$
$332$	−2.07237	+	9.07967i	−0.113736	+	0.498311i
$333$	3.49538	+	24.0090i	0.191546	+	1.31569i
$334$	33.3844	+	11.6817i	1.82671	+	0.639194i
$335$	21.1700	+	4.83190i	1.15664	+	0.263995i
$336$	−11.1326	+	18.3709i	−0.607333	+	1.00221i
$337$	8.26097	−	5.19071i	0.450004	−	0.282756i	−0.287902	−	0.957660i	$-0.592958\pi$
$337$	8.26097	−	5.19071i	0.450004	−	0.282756i	0.737906	+	0.674904i	$0.235815\pi$
$338$	−2.29971	+	20.4105i	−0.125088	+	1.11018i
$339$	7.14181	−	3.58285i	0.387890	−	0.194594i
$340$	5.30312	+	3.33217i	0.287602	+	0.180712i
$341$	7.36108	−	9.23050i	0.398625	−	0.499860i
$342$	2.03813	+	1.52010i	0.110209	+	0.0821975i
$343$	17.5337	+	8.44379i	0.946732	+	0.455922i
$344$	4.69203	−	3.74177i	0.252977	−	0.201743i
$345$	−26.5748	+	9.78450i	−1.43074	+	0.526780i
$346$	1.90499	+	5.44414i	0.102413	+	0.292679i
$347$	−13.9768			−0.750316			−0.375158	−	0.926961i	$-0.622412\pi$
$347$	−13.9768			−0.750316			−0.375158	+	0.926961i	$0.622412\pi$
$348$	7.17037	+	6.59139i	0.384372	+	0.353335i
$349$	−15.1394			−0.810391			−0.405196	−	0.914230i	$-0.632797\pi$
$349$	−15.1394			−0.810391			−0.405196	+	0.914230i	$0.632797\pi$
$350$	2.65186	+	7.57859i	0.141748	+	0.405093i
$351$	4.26414	+	3.86892i	0.227603	+	0.206508i
$352$	−5.10027	+	4.06733i	−0.271846	+	0.216790i
$353$	−15.0405	−	7.24310i	−0.800522	−	0.385511i	−0.0115449	−	0.999933i	$-0.503675\pi$
$353$	−15.0405	−	7.24310i	−0.800522	−	0.385511i	−0.788978	+	0.614422i	$0.789389\pi$
$354$	−5.46455	−	6.62932i	−0.290438	−	0.352344i
$355$	−9.46378	+	11.8672i	−0.502285	+	0.629846i
$356$	−8.28343	−	5.20483i	−0.439021	−	0.275855i
$357$	−6.51765	−	12.9918i	−0.344950	−	0.687601i
$358$	1.08287	−	9.61072i	0.0572314	−	0.507942i
$359$	4.93936	−	3.10361i	0.260690	−	0.163802i	−0.395346	−	0.918532i	$-0.629375\pi$
$359$	4.93936	−	3.10361i	0.260690	−	0.163802i	0.656035	+	0.754730i	$0.272232\pi$
$360$	8.46543	+	2.65794i	0.446167	+	0.140086i
$361$	−18.2936	−	4.17539i	−0.962821	−	0.219758i
$362$	12.9810	+	4.54225i	0.682266	+	0.238735i
$363$	−16.4348	−	1.58284i	−0.862602	−	0.0830776i
$364$	0.638870	−	2.79907i	0.0334859	−	0.146711i
$365$	1.87876	+	1.87876i	0.0983389	+	0.0983389i
$366$	5.80280	+	5.61793i	0.303317	+	0.293654i
$367$	2.23954	+	0.252336i	0.116903	+	0.0131718i	0.170222	−	0.985406i	$-0.445551\pi$
$367$	2.23954	+	0.252336i	0.116903	+	0.0131718i	−0.0533190	+	0.998578i	$0.516980\pi$
$368$	−44.9208	+	10.2529i	−2.34166	+	0.534469i
$369$	−2.12550	+	26.5691i	−0.110649	+	1.38313i
$370$	−19.5658	−	15.6032i	−1.01718	−	0.811170i
$371$	−12.6186	−	26.2028i	−0.655126	−	1.36038i
$372$	17.2460	+	3.64366i	0.894162	+	0.188915i
$373$	−19.9800	−	25.0542i	−1.03453	−	1.29726i	−0.953775	−	0.300522i	$-0.902839\pi$
$373$	−19.9800	−	25.0542i	−1.03453	−	1.29726i	−0.0807529	−	0.996734i	$-0.525732\pi$
$374$	−0.800330	−	7.10313i	−0.0413841	−	0.367294i
$375$	17.6452	−	11.4897i	0.911193	−	0.593325i
$376$		−	7.16659i		−	0.369589i
$377$	5.44139	+	2.44917i	0.280246	+	0.126139i
$378$	14.8632	+	16.8867i	0.764483	+	0.868556i
$379$	−9.87263	+	3.45458i	−0.507123	+	0.177450i	−0.571700	−	0.820463i	$-0.693716\pi$
$379$	−9.87263	+	3.45458i	−0.507123	+	0.177450i	0.0645770	+	0.997913i	$0.479430\pi$
$380$	−0.893920	+	0.100721i	−0.0458571	+	0.00516686i
$381$	−2.76189	+	3.58068i	−0.141496	+	0.183444i
$382$	7.06218	−	14.6648i	0.361333	−	0.750315i
$383$	−11.3746	+	5.47770i	−0.581213	+	0.279897i	−0.701300	−	0.712866i	$-0.747397\pi$
$383$	−11.3746	+	5.47770i	−0.581213	+	0.279897i	0.120087	+	0.992763i	$0.461683\pi$
$384$	18.5831	+	8.58146i	0.948315	+	0.437921i
$385$	−2.83630	+	4.51395i	−0.144551	+	0.230052i
$386$	−4.60462	−	20.1742i	−0.234369	−	1.02684i
$387$	−3.89364	−	10.0695i	−0.197925	−	0.511859i
$388$	−2.88902	−	4.59785i	−0.146668	−	0.233421i
$389$	5.76046	−	5.76046i	0.292067	−	0.292067i	−0.545829	−	0.837896i	$-0.683785\pi$
$389$	5.76046	−	5.76046i	0.292067	−	0.292067i	0.837896	+	0.545829i	$0.183785\pi$
$390$	−5.93813	+	0.0961195i	−0.300689	+	0.00486720i
$391$	10.2973	−	29.4280i	0.520756	−	1.48824i
$392$	0.464245	−	1.32673i	0.0234479	−	0.0670102i
$393$	−0.745801	+	0.0120721i	−0.0376207	+	0.000608959i
$394$	5.03164	−	5.03164i	0.253490	−	0.253490i
$395$	2.18723	+	3.48096i	0.110052	+	0.175146i
$396$	1.36862	+	3.53942i	0.0687756	+	0.177862i
$397$	−3.95989	−	17.3494i	−0.198741	−	0.870743i	−0.971687	−	0.236271i	$-0.924075\pi$
$397$	−3.95989	−	17.3494i	−0.198741	−	0.870743i	0.772946	−	0.634472i	$-0.218782\pi$
$398$	10.1860	−	16.2110i	0.510580	−	0.812583i
$399$	1.89535	+	0.875252i	0.0948863	+	0.0438174i
$400$	8.35131	−	4.02178i	0.417565	−	0.201089i
$401$	6.89266	−	14.3128i	0.344203	−	0.714745i	−0.654959	−	0.755664i	$-0.727314\pi$
$401$	6.89266	−	14.3128i	0.344203	−	0.714745i	0.999162	+	0.0409190i	$0.0130286\pi$
$402$	22.5981	−	29.2976i	1.12709	−	1.46123i
$403$	10.7314	−	1.20914i	0.534570	−	0.0602315i
$404$	11.9754	−	4.19036i	0.595797	−	0.208478i
$405$	9.12380	−	13.0972i	0.453365	−	0.650803i
$406$	20.0550	+	11.8894i	0.995314	+	0.590061i
$407$			9.79700i			0.485619i
$408$	−8.18610	+	5.33039i	−0.405272	+	0.263894i
$409$	1.02652	+	9.11057i	0.0507579	+	0.450489i	0.993227	+	0.116194i	$0.0370695\pi$
$409$	1.02652	+	9.11057i	0.0507579	+	0.450489i	−0.942469	+	0.334295i	$0.891502\pi$
$410$	−17.1414	−	21.4947i	−0.846555	−	1.06155i
$411$	−8.79113	−	1.85736i	−0.433635	−	0.0916166i
$412$	5.15117	+	10.6965i	0.253780	+	0.526980i
$413$	−5.51519	−	4.39822i	−0.271385	−	0.216422i
$414$	−3.84797	+	48.1003i	−0.189117	+	2.36400i
$415$	15.4215	−	3.51986i	0.757011	−	0.172783i
$416$	−5.92960	−	0.668105i	−0.290722	−	0.0327565i
$417$	−7.50254	−	7.26353i	−0.367401	−	0.355696i
$418$	0.725976	+	0.725976i	0.0355087	+	0.0355087i
$419$	3.95430	−	17.3249i	0.193180	−	0.846377i	−0.781701	−	0.623653i	$-0.785648\pi$
$419$	3.95430	−	17.3249i	0.193180	−	0.846377i	0.974881	−	0.222724i	$-0.0714950\pi$
$420$	−7.92260	−	0.763029i	−0.386583	−	0.0372320i
$421$	9.92465	+	3.47278i	0.483698	+	0.169253i	0.561102	−	0.827747i	$-0.310378\pi$
$421$	9.92465	+	3.47278i	0.483698	+	0.169253i	−0.0774043	+	0.997000i	$0.524663\pi$
$422$	−42.1519	−	9.62090i	−2.05192	−	0.468338i
$423$	−12.3002	−	3.86197i	−0.598058	−	0.187776i
$424$	−16.5499	+	10.3990i	−0.803735	+	0.505020i
$425$	−0.702250	+	6.23264i	−0.0340641	+	0.302327i
$426$	11.5976	+	23.1178i	0.561904	+	1.12006i
$427$	5.61526	+	3.52830i	0.271741	+	0.170746i
$428$	−0.779588	+	0.977572i	−0.0376828	+	0.0472527i
$429$	1.47882	+	1.79403i	0.0713981	+	0.0866165i
$430$	10.0330	+	4.83162i	0.483832	+	0.233001i
$431$	11.2015	−	8.93286i	0.539555	−	0.430281i	−0.315418	−	0.948953i	$-0.602145\pi$
$431$	11.2015	−	8.93286i	0.539555	−	0.430281i	0.854973	+	0.518672i	$0.173573\pi$
$432$	17.4510	−	19.2337i	0.839612	−	0.925381i
$433$	3.24108	+	9.26247i	0.155756	+	0.445126i	0.995147	−	0.0984033i	$-0.0313735\pi$
$433$	3.24108	+	9.26247i	0.155756	+	0.445126i	−0.839390	+	0.543529i	$0.817088\pi$
$434$	42.1941			2.02538
$435$	4.80246	−	15.8300i	0.230260	−	0.758990i
$436$	−11.0783			−0.530557
$437$	1.47901	+	4.22677i	0.0707507	+	0.202194i
$438$	4.24853	−	1.56426i	0.203003	−	0.0747430i
$439$	−30.2976	+	24.1616i	−1.44603	+	1.15317i	−0.485758	+	0.874093i	$0.661456\pi$
$439$	−30.2976	+	24.1616i	−1.44603	+	1.15317i	−0.960269	+	0.279075i	$0.909972\pi$
$440$	3.22804	+	1.55454i	0.153891	+	0.0741099i
$441$	−2.02694	−	1.51176i	−0.0965210	−	0.0719884i
$442$	4.07664	−	5.11195i	0.193906	−	0.243150i
$443$	16.3625	+	10.2813i	0.777408	+	0.488478i	0.861362	−	0.507992i	$-0.169612\pi$
$443$	16.3625	+	10.2813i	0.777408	+	0.488478i	−0.0839538	+	0.996470i	$0.526755\pi$
$444$	−13.0739	+	6.55881i	−0.620460	+	0.311268i
$445$	−1.86040	+	16.5115i	−0.0881912	+	0.782718i
$446$	−27.0834	+	17.0176i	−1.28244	+	0.805808i
$447$	3.95607	−	6.52826i	0.187116	−	0.308776i
$448$	1.45232	+	0.331483i	0.0686158	+	0.0156611i
$449$	0.404176	+	0.141427i	0.0190742	+	0.00667436i	0.339799	−	0.940498i	$-0.389641\pi$
$449$	0.404176	+	0.141427i	0.0190742	+	0.00667436i	−0.320725	+	0.947172i	$0.603927\pi$
$450$	−1.39852	−	9.60611i	−0.0659268	−	0.452837i
$451$	−2.39496	+	10.4930i	−0.112774	+	0.494096i
$452$	3.40613	+	3.40613i	0.160211	+	0.160211i
$453$	10.6412	−	10.9914i	0.499969	−	0.516421i
$454$	42.0924	+	4.74268i	1.97549	+	0.222585i
$455$	−4.75413	+	1.08510i	−0.222877	+	0.0508702i
$456$	0.441911	−	1.33166i	0.0206944	−	0.0623608i
$457$	−6.74257	−	5.37702i	−0.315404	−	0.251526i	0.452972	−	0.891525i	$-0.350364\pi$
$457$	−6.74257	−	5.37702i	−0.315404	−	0.251526i	−0.768376	+	0.639998i	$0.778935\pi$
$458$	4.67674	+	9.71134i	0.218530	+	0.453781i
$459$	4.73734	+	16.9225i	0.221120	+	0.789876i
$460$	−10.6445	−	13.3478i	−0.496305	−	0.622346i
$461$	3.41255	+	30.2872i	0.158938	+	1.41062i	0.779472	+	0.626437i	$0.215488\pi$
$461$	3.41255	+	30.2872i	0.158938	+	1.41062i	−0.620534	+	0.784180i	$0.713084\pi$
$462$	4.95677	+	7.61232i	0.230610	+	0.354157i
$463$			18.6575i			0.867086i	0.901133	+	0.433543i	$0.142737\pi$
$463$			18.6575i			0.867086i	−0.901133	+	0.433543i	$0.857263\pi$
$464$	11.0471	−	24.5437i	0.512851	−	1.13941i
$465$	−7.13342	−	29.0760i	−0.330804	−	1.34837i
$466$	22.3411	−	7.81750i	1.03493	−	0.362139i
$467$	18.2564	−	2.05701i	0.844807	−	0.0951869i	0.321058	−	0.947060i	$-0.395962\pi$
$467$	18.2564	−	2.05701i	0.844807	−	0.0951869i	0.523749	+	0.851873i	$0.324533\pi$
$468$	−1.40407	+	3.17451i	−0.0649031	+	0.146742i
$469$	13.1817	−	27.3720i	0.608673	−	1.26392i
$470$	11.9810	−	5.76976i	0.552644	−	0.266139i
$471$	7.37239	−	15.9649i	0.339702	−	0.735623i
$472$	−2.52232	+	4.01425i	−0.116099	+	0.184771i
$473$	−0.970062	−	4.25012i	−0.0446035	−	0.195421i
$474$	6.94746	−	0.896883i	0.319107	−	0.0411952i
$475$	−0.479289	−	0.762784i	−0.0219913	−	0.0349989i
$476$	6.19618	−	6.19618i	0.284001	−	0.284001i
$477$	8.92962	+	34.0090i	0.408859	+	1.55717i
$478$	−9.88842	+	28.2595i	−0.452286	+	1.29256i
$479$	−4.21591	+	12.0484i	−0.192630	+	0.550504i	−0.999173	−	0.0406714i	$-0.987050\pi$
$479$	−4.21591	+	12.0484i	−0.192630	+	0.550504i	0.806543	+	0.591176i	$0.201336\pi$
$480$	0.267732	+	16.5401i	0.0122202	+	0.754949i
$481$	−6.33668	+	6.33668i	−0.288928	+	0.288928i
$482$	−15.2032	−	24.1958i	−0.692488	−	1.10209i
$483$	5.07278	+	39.2949i	0.230819	+	1.78798i
$484$	−2.21494	−	9.70428i	−0.100679	−	0.441104i
$485$	−4.90690	+	7.80929i	−0.222811	+	0.354602i
$486$	−13.7432	−	23.4705i	−0.623402	−	1.06465i
$487$	−11.2965	+	5.44009i	−0.511892	+	0.246514i	−0.671954	−	0.740593i	$-0.734545\pi$
$487$	−11.2965	+	5.44009i	−0.511892	+	0.246514i	0.160062	+	0.987107i	$0.448831\pi$
$488$	1.93382	−	4.01562i	0.0875400	−	0.181779i
$489$	−5.58523	−	4.30806i	−0.252573	−	0.194817i
$490$	2.59178	−	0.292024i	0.117085	−	0.0131923i
$491$	−15.4772	+	5.41572i	−0.698477	+	0.244408i	−0.656078	−	0.754693i	$-0.727786\pi$
$491$	−15.4772	+	5.41572i	−0.698477	+	0.244408i	−0.0423993	+	0.999101i	$0.513500\pi$
$492$	−15.6061	+	3.82874i	−0.703576	+	0.172613i
$493$	10.0851	+	15.1651i	0.454209	+	0.683003i
$494$			0.939121i			0.0422530i
$495$	4.40766	−	4.70267i	0.198109	−	0.211369i
$496$	−5.45390	−	48.4047i	−0.244887	−	2.17343i
$497$	13.2408	+	16.6034i	0.593931	+	0.744765i
$498$	5.57159	−	26.3711i	0.249669	−	1.18172i
$499$	8.87570	+	18.4306i	0.397331	+	0.825066i	0.999641	+	0.0268037i	$0.00853291\pi$
$499$	8.87570	+	18.4306i	0.397331	+	0.825066i	−0.602310	+	0.798262i	$0.705753\pi$
$500$	9.92468	+	7.91467i	0.443845	+	0.353955i
$501$	−33.3245	−	11.0587i	−1.48883	−	0.494066i
$502$	−35.0630	+	8.00291i	−1.56494	+	0.357187i
$503$	0.689827	+	0.0777249i	0.0307579	+	0.00346558i	0.127330	−	0.991860i	$-0.459359\pi$
$503$	0.689827	+	0.0777249i	0.0307579	+	0.00346558i	−0.0965721	+	0.995326i	$0.530788\pi$
$504$	6.26103	−	10.7196i	0.278888	−	0.477487i
$505$	−15.2374	−	15.2374i	−0.678057	−	0.678057i
$506$	−4.33579	+	18.9963i	−0.192749	+	0.844490i
$507$	1.95472	−	20.2961i	0.0868124	−	0.901380i
$508$	−2.57324	−	0.900415i	−0.114169	−	0.0399495i
$509$	−14.3369	−	3.27230i	−0.635471	−	0.145042i	−0.107364	−	0.994220i	$-0.534241\pi$
$509$	−14.3369	−	3.27230i	−0.635471	−	0.145042i	−0.528107	+	0.849178i	$0.677098\pi$
$510$	−15.5019	−	9.39399i	−0.686434	−	0.415973i
$511$	3.14759	−	1.97776i	0.139241	−	0.0874910i
$512$	−1.14709	+	10.1807i	−0.0506945	+	0.449926i
$513$	−2.04744	−	1.47608i	−0.0903965	−	0.0651705i
$514$	−21.4838	−	13.4992i	−0.947611	−	0.595423i
$515$	12.5724	−	15.7653i	0.554007	−	0.694702i
$516$	5.02228	−	4.13987i	0.221093	−	0.182247i
$517$	−4.69033	−	2.25875i	−0.206281	−	0.0993395i
$518$	−27.3745	+	21.8304i	−1.20277	+	0.959174i
$519$	−1.97833	−	5.37316i	−0.0868390	−	0.235856i
$520$	1.08242	+	3.09337i	0.0474671	+	0.135653i
$521$	−10.8298			−0.474462			−0.237231	−	0.971453i	$-0.576240\pi$
$521$	−10.8298			−0.474462			−0.237231	+	0.971453i	$0.576240\pi$
$522$	−21.0578	−	18.7378i	−0.921675	−	0.820131i
$523$	5.85546			0.256041			0.128021	−	0.991771i	$-0.459138\pi$
$523$	5.85546			0.256041			0.128021	+	0.991771i	$0.459138\pi$
$524$	−0.148519	−	0.424444i	−0.00648810	−	0.0185419i
$525$	−2.75396	−	7.47978i	−0.120193	−	0.326444i
$526$	−12.7431	+	10.1623i	−0.555626	+	0.443097i
$527$	29.6964	+	14.3010i	1.29359	+	0.622962i
$528$	8.09208	−	6.67031i	0.352163	−	0.290288i
$529$	−38.6480	+	48.4630i	−1.68035	+	2.10709i
$530$	−30.7091	−	19.2958i	−1.33392	−	0.838157i
$531$	5.53054	+	6.49236i	0.240005	+	0.281744i
$532$	−0.140918	+	1.25069i	−0.00610959	+	0.0542241i
$533$	−8.33591	+	5.23780i	−0.361068	+	0.226874i
$534$	24.2138	+	14.6733i	1.04783	+	0.634977i
$535$	2.07045	+	0.472567i	0.0895134	+	0.0204308i
$536$	−19.2722	−	6.74362i	−0.832430	−	0.291280i
$537$	−0.920424	+	9.55685i	−0.0397192	+	0.412408i
$538$	2.13829	−	9.36846i	0.0921883	−	0.403903i
$539$	−0.721992	−	0.721992i	−0.0310984	−	0.0310984i
$540$	9.22642	+	2.73363i	0.397042	+	0.117637i
$541$	27.5408	+	3.10311i	1.18407	+	0.133413i	0.681960	−	0.731389i	$-0.261128\pi$
$541$	27.5408	+	3.10311i	1.18407	+	0.133413i	0.502112	+	0.864802i	$0.332556\pi$
$542$	36.9280	−	8.42857i	1.58619	−	0.362038i
$543$	−12.9577	−	4.30000i	−0.556069	−	0.184531i
$544$	−14.2388	−	11.3551i	−0.610486	−	0.486846i
$545$	8.16404	+	16.9528i	0.349709	+	0.726178i
$546$	−1.71761	+	8.12967i	−0.0735067	+	0.347918i
$547$	−18.6234	−	23.3530i	−0.796278	−	0.998502i	−0.999811	−	0.0194334i	$-0.993814\pi$
$547$	−18.6234	−	23.3530i	−0.796278	−	0.998502i	0.203533	−	0.979068i	$-0.434758\pi$
$548$	−0.606499	−	5.38283i	−0.0259084	−	0.229943i
$549$	−5.85003	−	5.48304i	−0.249673	−	0.234010i
$550$		−	3.91982i		−	0.167142i
$551$	−2.49058	−	0.799828i	−0.106102	−	0.0340738i
$552$	25.8612	−	6.34469i	1.10072	−	0.270048i
$553$	5.42907	−	1.89971i	0.230867	−	0.0807840i
$554$	42.3370	−	4.77024i	1.79873	−	0.202668i
$555$	19.6714	+	15.1731i	0.835002	+	0.644062i
$556$	2.73151	−	5.67204i	0.115842	−	0.240548i
$557$	20.5785	−	9.91006i	0.871937	−	0.419903i	0.0562642	−	0.998416i	$-0.482081\pi$
$557$	20.5785	−	9.91006i	0.871937	−	0.419903i	0.815673	+	0.578513i	$0.196367\pi$
$558$	−50.0757	−	9.73594i	−2.11987	−	0.412155i
$559$	2.12154	−	3.37641i	0.0897315	−	0.142807i
$560$	4.89441	+	21.4438i	0.206826	+	0.906166i
$561$	0.908519	+	7.03759i	0.0383577	+	0.297127i
$562$	−21.3097	−	33.9143i	−0.898897	−	1.43059i
$563$	−10.4785	+	10.4785i	−0.441617	+	0.441617i	−0.892555	−	0.450938i	$-0.851089\pi$
$563$	−10.4785	+	10.4785i	−0.441617	+	0.441617i	0.450938	+	0.892555i	$0.351089\pi$
$564$	−0.125793	−	7.77133i	−0.00529685	−	0.327232i
$565$	2.70218	−	7.72239i	0.113682	−	0.324883i
$566$	−15.2972	+	43.7170i	−0.642991	+	1.83756i
$567$	−15.0243	−	16.5226i	−0.630963	−	0.693885i
$568$	10.0922	−	10.0922i	0.423458	−	0.423458i
$569$	19.8489	+	31.5893i	0.832107	+	1.32429i	0.943789	+	0.330547i	$0.107233\pi$
$569$	19.8489	+	31.5893i	0.832107	+	1.32429i	−0.111682	+	0.993744i	$0.535624\pi$
$570$	2.58204	−	0.333329i	0.108150	−	0.0139616i
$571$	4.57150	+	20.0290i	0.191311	+	0.838189i	0.975908	+	0.218183i	$0.0700129\pi$
$571$	4.57150	+	20.0290i	0.191311	+	0.838189i	−0.784597	+	0.620007i	$0.787130\pi$
$572$	−0.745721	+	1.18681i	−0.0311801	+	0.0496229i
$573$	−6.77419	+	14.6695i	−0.282996	+	0.612826i
$574$	−34.6559	+	16.6894i	−1.44651	+	0.696602i
$575$	7.41810	−	15.4038i	0.309356	−	0.642385i
$576$	−1.64712	−	0.728513i	−0.0686300	−	0.0303547i
$577$	47.2544	−	5.32429i	1.96723	−	0.221653i	0.967691	−	0.252138i	$-0.0811336\pi$
$577$	47.2544	−	5.32429i	1.96723	−	0.221653i	0.999535	+	0.0304845i	$0.00970503\pi$
$578$	−9.16050	+	3.20540i	−0.381027	+	0.133327i
$579$	4.89461	+	19.9506i	0.203413	+	0.829118i
$580$	9.96957	−	0.257885i	0.413964	−	0.0107081i
$581$		−	22.1311i		−	0.918154i
$582$	8.57540	+	13.1696i	0.355462	+	0.545897i
$583$	1.58970	+	14.1090i	0.0658387	+	0.584334i
$584$	−1.55769	−	1.95328i	−0.0644576	−	0.0808273i
$585$	5.89255	−	0.190813i	0.243627	−	0.00788916i
$586$	14.3569	+	29.8125i	0.593080	+	1.23154i
$587$	14.0552	+	11.2086i	0.580119	+	0.462629i	0.869053	−	0.494720i	$-0.164729\pi$
$587$	14.0552	+	11.2086i	0.580119	+	0.462629i	−0.288934	+	0.957349i	$0.593301\pi$
$588$	0.480131	−	1.44684i	0.0198003	−	0.0596666i
$589$	−4.61545	+	1.05345i	−0.190176	+	0.0434065i
$590$	−8.74168	−	0.984951i	−0.359889	−	0.0405498i
$591$	−4.91348	+	5.07516i	−0.202114	+	0.208764i
$592$	28.5820	+	28.5820i	1.17471	+	1.17471i
$593$	7.33679	−	32.1446i	0.301286	−	1.32002i	−0.566903	−	0.823785i	$-0.691859\pi$
$593$	7.33679	−	32.1446i	0.301286	−	1.32002i	0.868189	−	0.496234i	$-0.165284\pi$
$594$	−4.12619	−	10.1780i	−0.169299	−	0.417608i
$595$	−14.0480	−	4.91560i	−0.575911	−	0.201520i
$596$	4.48655	+	1.02403i	0.183776	+	0.0419457i
$597$	−9.85004	+	16.2544i	−0.403135	+	0.665249i
$598$	−15.0912	+	9.48242i	−0.617124	+	0.387765i
$599$	0.0259349	−	0.230179i	0.00105967	−	0.00940485i	−0.993171	−	0.116666i	$-0.962779\pi$
$599$	0.0259349	−	0.230179i	0.00105967	−	0.00940485i	0.994231	+	0.107261i	$0.0342080\pi$
$600$	−4.78810	+	2.40206i	−0.195473	+	0.0980636i
$601$	5.17627	+	3.25247i	0.211144	+	0.132671i	0.633453	−	0.773781i	$-0.281637\pi$
$601$	5.17627	+	3.25247i	0.211144	+	0.132671i	−0.422308	+	0.906452i	$0.638780\pi$
$602$	9.71400	−	12.1810i	0.395913	−	0.496459i
$603$	−21.9598	+	29.4434i	−0.894271	+	1.19903i
$604$	8.30966	+	4.00172i	0.338115	+	0.162828i
$605$	−13.2178	+	10.5409i	−0.537382	+	0.428548i
$606$	−34.4571	+	12.6867i	−1.39973	+	0.515361i
$607$	−4.49999	−	12.8602i	−0.182649	−	0.521981i	0.815759	−	0.578393i	$-0.196320\pi$
$607$	−4.49999	−	12.8602i	−0.182649	−	0.521981i	−0.998408	+	0.0564117i	$0.982034\pi$
$608$	2.61583			0.106086
$609$	−20.0973	−	11.4790i	−0.814385	−	0.465153i
$610$	8.27018			0.334850
$611$	−1.57275	−	4.49465i	−0.0636266	−	0.181834i
$612$	−8.78330	+	5.92387i	−0.355044	+	0.239458i
$613$	21.5711	−	17.2023i	0.871247	−	0.694796i	−0.0821159	−	0.996623i	$-0.526168\pi$
$613$	21.5711	−	17.2023i	0.871247	−	0.694796i	0.953363	+	0.301826i	$0.0975963\pi$
$614$	−4.07681	−	1.96329i	−0.164527	−	0.0792319i
$615$	17.3597	+	21.0599i	0.700009	+	0.849215i
$616$	3.12542	−	3.91915i	0.125927	−	0.157907i
$617$	−12.3887	−	7.78436i	−0.498752	−	0.313387i	0.259058	−	0.965862i	$-0.416588\pi$
$617$	−12.3887	−	7.78436i	−0.498752	−	0.313387i	−0.757810	+	0.652475i	$0.773731\pi$
$618$	−15.4071	−	30.7115i	−0.619764	−	1.23540i
$619$	1.50822	−	13.3858i	0.0606205	−	0.538022i	−0.926297	−	0.376794i	$-0.877026\pi$
$619$	1.50822	−	13.3858i	0.0606205	−	0.538022i	0.986917	−	0.161227i	$-0.0515451\pi$
$620$	15.2824	−	9.60256i	0.613756	−	0.385648i
$621$	3.04662	−	47.8054i	0.122256	−	1.91836i
$622$	33.8958	+	7.73649i	1.35910	+	0.310205i
$623$	21.9428	+	7.67813i	0.879121	+	0.307618i
$624$	9.54829	+	0.919600i	0.382238	+	0.0368135i
$625$	2.73427	−	11.9796i	0.109371	−	0.479184i
$626$	−14.9646	−	14.9646i	−0.598105	−	0.598105i
$627$	−0.732256	−	0.708928i	−0.0292435	−	0.0283119i
$628$	10.5347	+	1.18698i	0.420381	+	0.0473656i
$629$	−26.6653	+	6.08619i	−1.06322	+	0.242672i
$630$	22.9616	+	1.83690i	0.914810	+	0.0731838i
$631$	−16.5679	−	13.2125i	−0.659558	−	0.525980i	0.235531	−	0.971867i	$-0.424317\pi$
$631$	−16.5679	−	13.2125i	−0.659558	−	0.525980i	−0.895089	+	0.445887i	$0.852888\pi$
$632$	−1.67724	−	3.48283i	−0.0667170	−	0.138539i
$633$	41.9939	+	8.87230i	1.66911	+	0.352642i
$634$	22.6614	+	28.4165i	0.899998	+	1.12856i
$635$	0.518440	+	4.60128i	0.0205737	+	0.182596i
$636$	−17.7639	+	11.5670i	−0.704385	+	0.458661i
$637$		−	0.933967i		−	0.0370051i
$638$	−7.32434	−	8.71237i	−0.289973	−	0.344926i
$639$	−11.8830	−	22.7600i	−0.470084	−	0.900373i
$640$	19.7829	−	6.92234i	0.781989	−	0.273630i
$641$	33.9080	−	3.82051i	1.33929	−	0.150901i	0.586919	−	0.809646i	$-0.300341\pi$
$641$	33.9080	−	3.82051i	1.33929	−	0.150901i	0.752367	+	0.658745i	$0.228912\pi$
$642$	2.21012	−	2.86534i	0.0872266	−	0.113086i
$643$	−8.94126	+	18.5667i	−0.352609	+	0.732200i	−0.999539	−	0.0303492i	$-0.990338\pi$
$643$	−8.94126	+	18.5667i	−0.352609	+	0.732200i	0.646931	+	0.762549i	$0.276052\pi$
$644$	−21.5207	+	10.3638i	−0.848036	+	0.408392i
$645$	−10.0362	−	4.63459i	−0.395174	−	0.182487i
$646$	−1.52495	+	2.42695i	−0.0599985	+	0.0954870i
$647$	8.36804	+	36.6628i	0.328982	+	1.44136i	0.821075	+	0.570821i	$0.193375\pi$
$647$	8.36804	+	36.6628i	0.328982	+	1.44136i	−0.492093	+	0.870543i	$0.663768\pi$
$648$	−9.90399	+	11.2772i	−0.389066	+	0.443011i
$649$	1.83224	+	2.91599i	0.0719216	+	0.114463i
$650$	2.53534	−	2.53534i	0.0994441	−	0.0994441i
$651$	−41.8812	+	0.677924i	−1.64145	+	0.0265699i
$652$	1.40449	−	4.01380i	0.0550040	−	0.157192i
$653$	12.3466	−	35.2847i	0.483161	−	1.38080i	−0.402055	−	0.915616i	$-0.631704\pi$
$653$	12.3466	−	35.2847i	0.483161	−	1.38080i	0.885216	−	0.465180i	$-0.154010\pi$
$654$	32.0577	−	0.518912i	1.25355	−	0.0202911i
$655$	−0.540062	+	0.540062i	−0.0211020	+	0.0211020i
$656$	23.6254	+	37.5996i	0.922418	+	1.46802i
$657$	−4.19189	+	1.62092i	−0.163541	+	0.0632379i
$658$	−4.14004	−	18.1387i	−0.161396	−	0.707121i
$659$	27.0994	−	43.1284i	1.05564	−	1.68005i	0.421502	−	0.906827i	$-0.361503\pi$
$659$	27.0994	−	43.1284i	1.05564	−	1.68005i	0.634140	−	0.773218i	$-0.281354\pi$
$660$	3.52772	+	1.62906i	0.137316	+	0.0634110i
$661$	7.29040	−	3.51087i	0.283564	−	0.136557i	−0.286696	−	0.958022i	$-0.592557\pi$
$661$	7.29040	−	3.51087i	0.283564	−	0.136557i	0.570259	+	0.821465i	$0.306843\pi$
$662$	13.3546	−	27.7311i	0.519041	−	1.07780i
$663$	−3.96428	+	5.13953i	−0.153960	+	0.199603i
$664$	−14.7802	+	1.66532i	−0.573581	+	0.0646271i
$665$	2.01773	−	0.706033i	0.0782441	−	0.0273788i
$666$	37.5251	−	19.5918i	1.45407	−	0.759166i
$667$	−12.2949	−	48.0983i	−0.476060	−	1.86237i
$668$		−	21.1676i		−	0.818999i
$669$	26.6091	−	17.3266i	1.02877	−	0.669884i
$670$	−4.24194	−	37.6482i	−0.163880	−	1.45448i
$671$	−2.01862	−	2.53126i	−0.0779278	−	0.0977184i
$672$	22.6444	+	4.78423i	0.873529	+	0.184556i
$673$	−4.56760	−	9.48471i	−0.176068	−	0.365609i	0.794195	−	0.607663i	$-0.207893\pi$
$673$	−4.56760	−	9.48471i	−0.176068	−	0.365609i	−0.970263	+	0.242055i	$0.922179\pi$
$674$	−13.3088	−	10.6134i	−0.512636	−	0.408813i
$675$	1.54249	+	9.51240i	0.0593703	+	0.366133i
$676$	11.9843	−	2.73533i	0.460934	−	0.105205i
$677$	−23.0750	−	2.59993i	−0.886846	−	0.0999235i	−0.343224	−	0.939254i	$-0.611519\pi$
$677$	−23.0750	−	2.59993i	−0.886846	−	0.0999235i	−0.543622	+	0.839330i	$0.682947\pi$
$678$	−10.0160	−	9.69687i	−0.384661	−	0.372406i
$679$	9.12439	+	9.12439i	0.350162	+	0.350162i
$680$	−2.22578	+	9.75177i	−0.0853546	+	0.373963i
$681$	−41.8565	−	4.03121i	−1.60394	−	0.154476i
$682$	−19.4432	−	6.80346i	−0.744517	−	0.260518i
$683$	−14.9652	−	3.41570i	−0.572627	−	0.130698i	−0.0736044	−	0.997288i	$-0.523450\pi$
$683$	−14.9652	−	3.41570i	−0.572627	−	0.130698i	−0.499022	+	0.866589i	$0.666307\pi$
$684$	0.455826	−	1.45179i	0.0174289	−	0.0555106i
$685$	−7.79020	+	4.89491i	−0.297648	+	0.187025i
$686$	3.80173	−	33.7413i	0.145151	−	1.28825i
$687$	−4.79808	−	9.56418i	−0.183058	−	0.364896i
$688$	−15.2295	−	9.56932i	−0.580619	−	0.364827i
$689$	−8.09745	+	10.1539i	−0.308488	+	0.386832i
$690$	31.4276	+	38.1264i	1.19643	+	1.45145i
$691$	14.5662	+	7.01469i	0.554123	+	0.266852i	0.689921	−	0.723885i	$-0.257645\pi$
$691$	14.5662	+	7.01469i	0.554123	+	0.266852i	−0.135798	+	0.990737i	$0.543360\pi$
$692$	2.69880	−	2.15222i	0.102593	−	0.0818152i
$693$	−5.04232	−	7.47623i	−0.191542	−	0.283998i
$694$	8.05427	+	23.0178i	0.305736	+	0.873744i
$695$	−10.6927			−0.405596
$696$	−6.15391	+	14.2857i	−0.233263	+	0.541497i
$697$	−30.0475			−1.13813
$698$	8.72419	+	24.9323i	0.330215	+	0.943701i
$699$	−22.0498	+	8.11847i	−0.834002	+	0.307069i
$700$	3.75690	−	2.99603i	0.141998	−	0.113239i
$701$	28.6080	+	13.7769i	1.08051	+	0.520346i	0.887479	−	0.460847i	$-0.152454\pi$
$701$	28.6080	+	13.7769i	1.08051	+	0.520346i	0.193029	+	0.981193i	$0.438169\pi$
$702$	3.91430	−	9.25192i	0.147736	−	0.349191i
$703$	2.44936	−	3.07140i	0.0923792	−	0.115840i
$704$	−0.615785	−	0.386923i	−0.0232083	−	0.0145827i
$705$	−11.7995	+	5.91947i	−0.444394	+	0.222940i
$706$	−3.26113	+	28.9433i	−0.122734	+	1.08930i
$707$	−25.5281	+	16.0404i	−0.960083	+	0.603260i
$708$	−2.66470	+	4.39726i	−0.100146	+	0.165259i
$709$	0.0799658	+	0.0182517i	0.00300318	+	0.000685456i	0.224022	−	0.974584i	$-0.428081\pi$
$709$	0.0799658	+	0.0182517i	0.00300318	+	0.000685456i	−0.221019	+	0.975269i	$0.570938\pi$
$710$	24.9971	+	8.74687i	0.938125	+	0.328264i
$711$	−6.88152	+	1.00186i	−0.258077	+	0.0375725i
$712$	3.47664	−	15.2322i	0.130293	−	0.570850i
$713$	−63.5311	−	63.5311i	−2.37926	−	2.37926i
$714$	−17.6398	+	18.2203i	−0.660153	+	0.681876i
$715$	2.36568	+	0.266548i	0.0884713	+	0.00996832i
$716$	−5.64306	+	1.28799i	−0.210891	+	0.0481345i
$717$	9.36105	−	28.2088i	0.349595	−	1.05348i
$718$	−7.95753	−	6.34592i	−0.296973	−	0.236828i
$719$	6.89173	+	14.3108i	0.257018	+	0.533704i	0.989053	−	0.147564i	$-0.0471432\pi$
$719$	6.89173	+	14.3108i	0.257018	+	0.533704i	−0.732034	+	0.681268i	$0.761429\pi$
$720$	−0.860675	−	26.5787i	−0.0320755	−	0.990529i
$721$	−17.5901	−	22.0573i	−0.655089	−	0.821456i
$722$	3.66558	+	32.5330i	0.136419	+	1.21075i
$723$	15.4792	+	23.7721i	0.575679	+	0.884094i
$724$		−	8.23069i		−	0.305891i
$725$	4.56451	+	8.88309i	0.169522	+	0.329910i
$726$	6.86397	+	27.9778i	0.254746	+	1.03835i
$727$	−4.29705	+	1.50360i	−0.159369	+	0.0557655i	−0.408784	−	0.912631i	$-0.634047\pi$
$727$	−4.29705	+	1.50360i	−0.159369	+	0.0557655i	0.249416	+	0.968397i	$0.419761\pi$
$728$	4.55642	−	0.513385i	0.168872	−	0.0190273i
$729$	14.0183	+	23.0757i	0.519197	+	0.854654i
$730$	2.01139	−	4.17670i	0.0744450	−	0.154587i
$731$	10.9653	−	5.28060i	0.405566	−	0.195310i
$732$	2.02652	−	4.38841i	0.0749022	−	0.162200i
$733$	−9.11220	+	14.5020i	−0.336567	+	0.535643i	−0.971535	−	0.236895i	$-0.923870\pi$
$733$	−9.11220	+	14.5020i	−0.336567	+	0.535643i	0.634968	+	0.772538i	$0.281013\pi$
$734$	−0.874997	−	3.83361i	−0.0322967	−	0.141501i
$735$	−2.56787	+	0.331500i	−0.0947173	+	0.0122275i
$736$	26.4124	+	42.0351i	0.973574	+	1.54943i
$737$	−10.4877	+	10.4877i	−0.386318	+	0.386318i
$738$	44.9803	−	11.8103i	1.65575	−	0.434743i
$739$	4.94780	−	14.1400i	0.182008	−	0.520148i	−0.816342	−	0.577568i	$-0.804002\pi$
$739$	4.94780	−	14.1400i	0.182008	−	0.520148i	0.998350	+	0.0574202i	$0.0182875\pi$
$740$	−4.94665	+	14.1367i	−0.181842	+	0.519676i
$741$	−0.0150887	−	0.932156i	−0.000554296	−	0.0342436i
$742$	−35.8806	+	35.8806i	−1.31722	+	1.31722i
$743$	5.32655	+	8.47716i	0.195412	+	0.310997i	0.930029	−	0.367485i	$-0.119781\pi$
$743$	5.32655	+	8.47716i	0.195412	+	0.310997i	−0.734617	+	0.678482i	$0.762638\pi$
$744$	3.60423	+	27.9192i	0.132137	+	1.02357i
$745$	−1.73927	−	7.62024i	−0.0637220	−	0.279184i
$746$	−29.7469	+	47.3419i	−1.08911	+	1.73331i
$747$	−5.10657	+	26.2651i	−0.186840	+	0.960989i
$748$	−3.85430	+	1.85613i	−0.140927	+	0.0678669i
$749$	1.28918	−	2.67702i	0.0471058	−	0.0978162i
$750$	−29.0900	−	22.4380i	−1.06222	−	0.819320i
$751$	−0.260316	+	0.0293306i	−0.00949907	+	0.00107029i	−0.116713	−	0.993166i	$-0.537236\pi$
$751$	−0.260316	+	0.0293306i	−0.00949907	+	0.00107029i	0.107214	+	0.994236i	$0.465807\pi$
$752$	−20.2734	+	7.09398i	−0.739295	+	0.258691i
$753$	34.6744	−	8.50691i	1.26361	−	0.310009i
$754$	0.897778	−	10.3725i	0.0326951	−	0.377745i
$755$		−	15.6650i		−	0.570107i
$756$	6.60119	−	11.7340i	0.240083	−	0.426762i
$757$	4.38898	+	38.9533i	0.159520	+	1.41578i	0.777151	+	0.629314i	$0.216664\pi$
$757$	4.38898	+	38.9533i	0.159520	+	1.41578i	−0.617631	+	0.786468i	$0.711907\pi$
$758$	11.3784	+	14.2680i	0.413281	+	0.518239i
$759$	3.99842	−	18.9251i	0.145134	−	0.686938i
$760$	−0.623351	−	1.29440i	−0.0226113	−	0.0469529i
$761$	−18.6302	−	14.8571i	−0.675344	−	0.538569i	0.224667	−	0.974436i	$-0.427871\pi$
$761$	−18.6302	−	14.8571i	−0.675344	−	0.538569i	−0.900011	+	0.435867i	$0.856442\pi$
$762$	7.48842	+	2.48502i	0.271277	+	0.0900228i
$763$	25.6657	−	5.85803i	0.929161	−	0.212075i
$764$	−9.67994	−	1.09067i	−0.350208	−	0.0394590i
$765$	15.5378	+	9.07526i	0.561771	+	0.328117i
$766$	15.5757	+	15.5757i	0.562771	+	0.562771i
$767$	−0.700969	+	3.07114i	−0.0253105	+	0.110893i
$768$	3.22435	−	33.4787i	0.116349	−	1.20806i
$769$	−2.11272	−	0.739272i	−0.0761865	−	0.0266588i	0.291917	−	0.956444i	$-0.405707\pi$
$769$	−2.11272	−	0.739272i	−0.0761865	−	0.0266588i	−0.368103	+	0.929785i	$0.619993\pi$
$770$	9.06825	+	2.06977i	0.326797	+	0.0745893i
$771$	21.5414	+	13.0539i	0.775794	+	0.470125i
$772$	−10.4860	+	6.58882i	−0.377401	+	0.237137i
$773$	−0.614691	+	5.45554i	−0.0221089	+	0.196222i	−0.999911	−	0.0133064i	$-0.995764\pi$
$773$	−0.614691	+	5.45554i	−0.0221089	+	0.196222i	0.977803	+	0.209528i	$0.0671929\pi$
$774$	−14.3392	+	12.2149i	−0.515411	+	0.439055i
$775$	15.3043	+	9.61632i	0.549746	+	0.345428i
$776$	5.40709	−	6.78027i	0.194103	−	0.243398i
$777$	26.8207	−	22.1084i	0.962189	−	0.793133i
$778$	−12.8062	−	6.16712i	−0.459123	−	0.221102i
$779$	3.37419	−	2.69083i	0.120893	−	0.0964090i
$780$	1.22805	+	3.33540i	0.0439713	+	0.119426i
$781$	−3.42422	−	9.78587i	−0.122528	−	0.350166i
$782$	−54.3974			−1.94525
$783$	21.2027	+	18.2605i	0.757722	+	0.652577i
$784$	−4.21271			−0.150454
$785$	−5.94703	−	16.9956i	−0.212259	−	0.606601i
$786$	0.449655	+	1.22127i	0.0160387	+	0.0435612i
$787$	−20.8008	+	16.5881i	−0.741469	+	0.591302i	−0.919670	−	0.392692i	$-0.871544\pi$
$787$	−20.8008	+	16.5881i	−0.741469	+	0.591302i	0.178201	+	0.983994i	$0.442972\pi$
$788$	−3.83690	−	1.84775i	−0.136684	−	0.0658235i
$789$	12.4853	−	10.2917i	0.444490	−	0.366393i
$790$	4.47222	−	5.60799i	0.159114	−	0.199523i
$791$	−9.69225	−	6.09005i	−0.344617	−	0.216537i
$792$	−4.61354	+	3.93006i	−0.163935	+	0.139649i
$793$	0.331580	−	2.94286i	0.0117748	−	0.104504i
$794$	−26.2900	+	16.5191i	−0.932998	+	0.586242i
$795$	30.7914	+	18.6593i	1.09206	+	0.661778i
$796$	−11.1709	−	2.54968i	−0.395941	−	0.0903709i
$797$	−3.37422	−	1.18069i	−0.119521	−	0.0418222i	0.269856	−	0.962901i	$-0.413024\pi$
$797$	−3.37422	−	1.18069i	−0.119521	−	0.0418222i	−0.389377	+	0.921078i	$0.627310\pi$
$798$	0.349197	−	3.62574i	0.0123614	−	0.128350i
$799$	3.23405	−	14.1693i	0.114412	−	0.501273i
$800$	−7.06194	−	7.06194i	−0.249677	−	0.249677i
$801$	−24.2699	−	14.1755i	−0.857536	−	0.500866i
$802$	−27.5430	−	3.10335i	−0.972576	−	0.109583i
$803$	−1.76932	+	0.403835i	−0.0624378	+	0.0142510i
$804$	−21.0168	−	6.97439i	−0.741204	−	0.245968i
$805$	31.7188	+	25.2949i	1.11794	+	0.891528i
$806$	−8.17534	−	16.9763i	−0.287964	−	0.597964i
$807$	−1.97191	+	9.33334i	−0.0694146	+	0.328549i
$808$	12.6334	+	15.8418i	0.444442	+	0.557313i
$809$	−0.733011	−	6.50565i	−0.0257713	−	0.228727i	−0.999995	−	0.00314277i	$-0.999000\pi$
$809$	−0.733011	−	6.50565i	−0.0257713	−	0.228727i	0.974224	−	0.225584i	$-0.0724289\pi$
$810$	−26.8268	−	7.47820i	−0.942597	−	0.262757i
$811$		−	30.0526i		−	1.05529i	−0.849465	−	0.527645i	$-0.823075\pi$
$811$		−	30.0526i		−	1.05529i	0.849465	−	0.527645i	$-0.176925\pi$
$812$	2.75206	−	13.6790i	0.0965784	−	0.480040i
$813$	−36.5187	+	8.95938i	−1.28077	+	0.314219i
$814$	16.1342	−	5.64561i	0.565504	−	0.197878i
$815$	−7.17719	+	0.808675i	−0.251406	+	0.0283266i
$816$	23.1822	+	17.8811i	0.811539	+	0.625964i
$817$	−0.758459	+	1.57496i	−0.0265351	+	0.0551007i
$818$	14.4122	−	6.94057i	0.503912	−	0.242671i
$819$	1.57425	−	8.09698i	0.0550087	−	0.282931i
$820$	−8.75391	+	13.9318i	−0.305700	+	0.486518i
$821$	7.11158	+	31.1579i	0.248196	+	1.08742i	0.933336	+	0.359005i	$0.116884\pi$
$821$	7.11158	+	31.1579i	0.248196	+	1.08742i	−0.685140	+	0.728412i	$0.740259\pi$
$822$	2.00717	+	15.5480i	0.0700083	+	0.542299i
$823$	−10.7333	−	17.0819i	−0.374139	−	0.595439i	0.605587	−	0.795779i	$-0.292938\pi$
$823$	−10.7333	−	17.0819i	−0.374139	−	0.595439i	−0.979726	+	0.200340i	$0.935795\pi$
$824$	−13.4072	+	13.4072i	−0.467063	+	0.467063i
$825$	0.0629790	+	3.89075i	0.00219265	+	0.135459i
$826$	−4.06504	+	11.6172i	−0.141441	+	0.404215i
$827$	8.59715	−	24.5693i	0.298952	−	0.854357i	−0.692209	−	0.721697i	$-0.743363\pi$
$827$	8.59715	−	24.5693i	0.298952	−	0.854357i	0.991162	−	0.132660i	$-0.0423518\pi$
$828$	27.9320	−	7.33401i	0.970705	−	0.254874i
$829$	3.76700	−	3.76700i	0.130833	−	0.130833i	−0.638658	−	0.769491i	$-0.720510\pi$
$829$	3.76700	−	3.76700i	0.130833	−	0.130833i	0.769491	+	0.638658i	$0.220510\pi$
$830$	−14.6835	−	23.3686i	−0.509670	−	0.811135i
$831$	−41.9464	+	5.41508i	−1.45511	+	0.187847i
$832$	−0.148027	−	0.648550i	−0.00513192	−	0.0224844i
$833$	1.51658	−	2.41363i	0.0525465	−	0.0836273i
$834$	−7.63855	+	16.5413i	−0.264502	+	0.572777i
$835$	−32.3920	+	15.5992i	−1.12097	+	0.539832i
$836$	0.266598	−	0.553597i	0.00922049	−	0.0191466i
$837$	49.8608	+	8.85918i	1.72344	+	0.306218i
$838$	−30.8103	+	3.47148i	−1.06432	+	0.119920i
$839$	−45.6449	+	15.9718i	−1.57584	+	0.551409i	−0.969773	−	0.244008i	$-0.921538\pi$
$839$	−45.6449	+	15.9718i	−1.57584	+	0.551409i	−0.606063	+	0.795417i	$0.707252\pi$
$840$	−3.02876	−	12.3453i	−0.104502	−	0.425953i
$841$	26.7437	+	11.2150i	0.922196	+	0.386724i
$842$		−	18.3457i		−	0.632233i
$843$	21.6966	+	33.3204i	0.747271	+	1.14761i
$844$	2.89715	+	25.7130i	0.0997242	+	0.885076i
$845$	−13.0174	−	16.3233i	−0.447813	−	0.561540i
$846$	0.728021	+	22.4822i	0.0250299	+	0.772953i
$847$	10.2629	+	21.3111i	0.352638	+	0.732260i
$848$	45.7997	+	36.5241i	1.57277	+	1.25424i
$849$	14.4814	−	43.6386i	0.497001	−	1.49767i
$850$	10.6689	−	2.43511i	0.365941	−	0.0835236i
$851$	74.0872	+	8.34762i	2.53968	+	0.286153i
$852$	10.7666	−	11.1209i	0.368859	−	0.380997i
$853$	−13.2989	−	13.2989i	−0.455345	−	0.455345i	0.441779	−	0.897124i	$-0.354347\pi$
$853$	−13.2989	−	13.2989i	−0.455345	−	0.455345i	−0.897124	+	0.441779i	$0.854347\pi$
$854$	2.57475	−	11.2807i	0.0881062	−	0.386018i
$855$	−2.55754	+	0.372342i	−0.0874659	+	0.0127338i
$856$	−1.88484	−	0.659535i	−0.0644226	−	0.0225424i
$857$	−21.8609	−	4.98961i	−0.746754	−	0.170442i	−0.167822	−	0.985817i	$-0.553673\pi$
$857$	−21.8609	−	4.98961i	−0.746754	−	0.170442i	−0.578932	+	0.815375i	$0.696531\pi$
$858$	2.10232	−	3.46922i	0.0717720	−	0.118437i
$859$	18.0755	−	11.3576i	0.616730	−	0.387517i	−0.187131	−	0.982335i	$-0.559919\pi$
$859$	18.0755	−	11.3576i	0.616730	−	0.387517i	0.803860	+	0.594818i	$0.202776\pi$
$860$	0.746184	−	6.62257i	0.0254447	−	0.225828i
$861$	34.1307	−	17.1224i	1.16317	−	0.583531i
$862$	−21.1660	−	13.2995i	−0.720918	−	0.452983i
$863$	23.5034	−	29.4724i	0.800066	−	1.00325i	−0.199660	−	0.979865i	$-0.563984\pi$
$863$	23.5034	−	29.4724i	0.800066	−	1.00325i	0.999727	−	0.0233862i	$-0.00744473\pi$
$864$	−25.7704	−	10.9029i	−0.876726	−	0.370924i
$865$	−5.28231	−	2.54383i	−0.179604	−	0.0864927i
$866$	13.3862	−	10.6752i	0.454882	−	0.362757i
$867$	9.04107	−	3.32881i	0.307051	−	0.113052i
$868$	−8.34026	−	23.8351i	−0.283087	−	0.809016i
$869$	−2.80804			−0.0952562
$870$	−28.8371	+	1.21323i	−0.977670	+	0.0411322i
$871$	−13.5668			−0.459694
$872$	−5.84355	−	16.6999i	−0.197888	−	0.565531i
$873$	−8.72339	−	12.9341i	−0.295242	−	0.437755i
$874$	6.10858	−	4.87143i	0.206626	−	0.164778i
$875$	−27.1781	−	13.0883i	−0.918787	−	0.442465i
$876$	−1.72342	−	2.09076i	−0.0582288	−	0.0706403i
$877$	16.0258	−	20.0958i	0.541154	−	0.678586i	−0.433796	−	0.901011i	$-0.642826\pi$
$877$	16.0258	−	20.0958i	0.541154	−	0.678586i	0.974950	+	0.222425i	$0.0713974\pi$
$878$	57.2498	+	35.9724i	1.93209	+	1.21401i
$879$	−14.7295	−	29.3607i	−0.496812	−	0.990313i
$880$	1.20228	−	10.6705i	0.0405289	−	0.359704i
$881$	−43.6456	+	27.4243i	−1.47046	+	0.923949i	−0.471339	+	0.881952i	$0.656229\pi$
$881$	−43.6456	+	27.4243i	−1.47046	+	0.923949i	−0.999118	+	0.0419974i	$0.986628\pi$
$882$	−1.32160	+	4.20924i	−0.0445005	+	0.141732i
$883$	−3.39773	−	0.775510i	−0.114343	−	0.0260980i	0.164967	−	0.986299i	$-0.447248\pi$
$883$	−3.39773	−	0.775510i	−0.114343	−	0.0260980i	−0.279309	+	0.960201i	$0.590106\pi$
$884$	−3.69350	−	1.29241i	−0.124226	−	0.0434685i
$885$	8.69268	+	0.837196i	0.292201	+	0.0281420i
$886$	7.50268	−	32.8714i	0.252057	−	1.10434i
$887$	21.7214	+	21.7214i	0.729332	+	0.729332i	0.970487	−	0.241155i	$-0.0775262\pi$
$887$	21.7214	+	21.7214i	0.729332	+	0.729332i	−0.241155	+	0.970487i	$0.577526\pi$
$888$	−16.7832	−	16.2485i	−0.563206	−	0.545264i
$889$	6.43766	+	0.725351i	0.215912	+	0.0243275i
$890$	28.2640	−	6.45108i	0.947412	−	0.216241i
$891$	4.25911	+	10.0362i	0.142686	+	0.336226i
$892$	14.9665	+	11.9354i	0.501116	+	0.399627i
$893$	0.905726	+	1.88076i	0.0303090	+	0.0629372i
$894$	−13.0308	−	2.75310i	−0.435815	−	0.0920773i
$895$	6.12954	+	7.68620i	0.204888	+	0.256921i
$896$	−3.28323	−	29.1395i	−0.109685	−	0.973483i
$897$	14.8269	−	9.65456i	0.495056	−	0.322356i
$898$		−	0.747116i		−	0.0249316i
$899$	51.9844	−	7.22298i	1.73378	−	0.240900i
$900$	−5.14997	+	2.68879i	−0.171666	+	0.0896265i
$901$	−37.4140	+	13.0917i	−1.24644	+	0.436149i
$902$	18.6605	−	2.10254i	0.621328	−	0.0700068i
$903$	−9.44625	+	12.2467i	−0.314352	+	0.407545i
$904$	−3.33788	+	6.93119i	−0.111016	+	0.230528i
$905$	−12.5951	+	6.06550i	−0.418676	+	0.201624i
$906$	−24.2333	−	11.1907i	−0.805098	−	0.371784i
$907$	8.72468	−	13.8852i	0.289698	−	0.461052i	−0.669890	−	0.742460i	$-0.733659\pi$
$907$	8.72468	−	13.8852i	0.289698	−	0.461052i	0.959588	+	0.281408i	$0.0908016\pi$
$908$	−5.64106	−	24.7151i	−0.187205	−	0.820199i
$909$	33.9978	−	13.1462i	1.12763	−	0.436032i
$910$	4.52661	+	7.20405i	0.150056	+	0.238812i
$911$	−11.4146	+	11.4146i	−0.378182	+	0.378182i	−0.870446	−	0.492264i	$-0.836170\pi$
$911$	−11.4146	+	11.4146i	−0.378182	+	0.378182i	0.492264	+	0.870446i	$0.336170\pi$
$912$	−4.20455	+	0.0680583i	−0.139227	+	0.00225364i
$913$	−3.56846	+	10.1981i	−0.118099	+	0.337507i
$914$	−4.96970	+	14.2026i	−0.164383	+	0.469779i
$915$	−8.20885	+	0.132875i	−0.271376	+	0.00439272i
$916$	4.56143	−	4.56143i	0.150714	−	0.150714i
$917$	0.568520	+	0.904795i	0.0187742	+	0.0298790i
$918$	25.1390	−	17.5535i	0.829710	−	0.579351i
$919$	0.854390	+	3.74333i	0.0281837	+	0.123481i	0.987063	−	0.160334i	$-0.0512571\pi$
$919$	0.854390	+	3.74333i	0.0281837	+	0.123481i	−0.958879	+	0.283815i	$0.908400\pi$
$920$	14.5063	−	23.0866i	0.478259	−	0.761144i
$921$	4.07812	+	1.88323i	0.134379	+	0.0620545i
$922$	47.9121	−	23.0733i	1.57790	−	0.759877i
$923$	4.11470	−	8.54427i	0.135437	−	0.281238i
$924$	3.32036	−	4.30472i	0.109232	−	0.141615i
$925$	−14.9043	+	1.67931i	−0.490051	+	0.0552155i
$926$	30.7261	−	10.7515i	1.00972	−	0.353317i
$927$	15.7863	+	30.2362i	0.518489	+	0.993087i
$928$	−28.8917	−	2.50068i	−0.948417	−	0.0820887i
$929$			40.7797i			1.33794i	0.743290	+	0.668970i	$0.233264\pi$
$929$			40.7797i			1.33794i	−0.743290	+	0.668970i	$0.766736\pi$
$930$	−43.7732	+	28.5030i	−1.43538	+	0.934650i
$931$	0.0458413	+	0.406853i	0.00150239	+	0.0133341i
$932$	−8.83208	−	11.0751i	−0.289304	−	0.362776i
$933$	−33.7687	−	7.13452i	−1.10554	−	0.233574i
$934$	−13.9080	−	28.8803i	−0.455084	−	0.944992i
$935$	5.68075	+	4.53024i	0.185780	+	0.148155i
$936$	−5.52599	−	0.442073i	−0.180623	−	0.0144496i
$937$	−31.6163	+	7.21621i	−1.03286	+	0.235743i	−0.705167	−	0.709041i	$-0.749128\pi$
$937$	−31.6163	+	7.21621i	−1.03286	+	0.235743i	−0.327692	+	0.944785i	$0.606271\pi$
$938$	−52.6737	−	5.93490i	−1.71986	−	0.193781i
$939$	15.0940	+	14.6132i	0.492576	+	0.476883i
$940$	−5.62751	−	5.62751i	−0.183549	−	0.183549i
$941$	−1.18385	+	5.18681i	−0.0385926	+	0.169085i	−0.990552	−	0.137140i	$-0.956209\pi$
$941$	−1.18385	+	5.18681i	−0.0385926	+	0.169085i	0.951959	+	0.306225i	$0.0990661\pi$
$942$	−30.5402	−	2.94134i	−0.995054	−	0.0958341i
$943$	77.3098	+	27.0519i	2.51755	+	0.880931i
$944$	13.8526	+	3.16176i	0.450863	+	0.102907i
$945$	−22.8208	−	1.45436i	−0.742360	−	0.0473103i
$946$	−6.44032	+	4.04672i	−0.209393	+	0.131570i
$947$	5.03475	−	44.6846i	0.163607	−	1.45205i	−0.596686	−	0.802475i	$-0.703516\pi$
$947$	5.03475	−	44.6846i	0.163607	−	1.45205i	0.760293	−	0.649580i	$-0.225055\pi$
$948$	−1.87990	−	3.74728i	−0.0610564	−	0.121706i
$949$	−1.40559	−	0.883191i	−0.0456274	−	0.0286696i
$950$	−0.979999	+	1.22888i	−0.0317954	+	0.0398701i
$951$	−22.9499	−	27.8416i	−0.744201	−	0.902827i
$952$	12.6087	+	6.07202i	0.408650	+	0.196795i
$953$	−27.9048	+	22.2534i	−0.903926	+	0.720857i	−0.960717	−	0.277529i	$-0.910485\pi$
$953$	−27.9048	+	22.2534i	−0.903926	+	0.720857i	0.0567912	+	0.998386i	$0.481913\pi$
$954$	50.8620	−	34.3037i	1.64672	−	1.11062i
$955$	5.46449	+	15.6166i	0.176827	+	0.505342i
$956$	17.9181			0.579513
$957$	7.41000	+	8.53008i	0.239531	+	0.275738i
$958$	22.2714			0.719555
$959$	4.25145	+	12.1499i	0.137286	+	0.392342i
$960$	−1.73060	+	0.637184i	−0.0558548	+	0.0205650i
$961$	50.0252	−	39.8937i	1.61371	−	1.28689i
$962$	14.0872	+	6.78402i	0.454188	+	0.218725i
$963$	−2.14770	+	2.87960i	−0.0692085	+	0.0927939i
$964$	−10.6629	+	13.3708i	−0.343428	+	0.430645i
$965$	17.8102	+	11.1909i	0.573330	+	0.360247i
$966$	61.7896	−	30.9981i	1.98805	−	0.997348i
$967$	−3.77346	+	33.4904i	−0.121346	+	1.07698i	0.774487	+	0.632589i	$0.218008\pi$
$967$	−3.77346	+	33.4904i	−0.121346	+	1.07698i	−0.895834	+	0.444389i	$0.853421\pi$
$968$	13.4603	−	8.45765i	0.432630	−	0.271839i
$969$	1.47465	−	2.43345i	0.0473726	−	0.0781737i
$970$	15.6884	+	3.58077i	0.503724	+	0.114972i
$971$	−16.1225	−	5.64150i	−0.517395	−	0.181044i	0.0589345	−	0.998262i	$-0.481230\pi$
$971$	−16.1225	−	5.64150i	−0.517395	−	0.181044i	−0.576329	+	0.817218i	$0.695515\pi$
$972$	−10.5418	+	12.4027i	−0.338128	+	0.397816i
$973$	−3.32894	+	14.5850i	−0.106721	+	0.467575i
$974$	15.4687	+	15.4687i	0.495650	+	0.495650i
$975$	−2.47580	+	2.55727i	−0.0792890	+	0.0818981i
$976$	−13.2739	−	1.49561i	−0.424888	−	0.0478734i
$977$	−20.1415	+	4.59718i	−0.644385	+	0.147077i	−0.532211	−	0.846612i	$-0.678639\pi$
$977$	−20.1415	+	4.59718i	−0.644385	+	0.147077i	−0.112174	+	0.993689i	$0.535782\pi$
$978$	−3.87619	+	11.6806i	−0.123947	+	0.373505i
$979$	−8.87328	−	7.07620i	−0.283591	−	0.226156i
$980$	−0.677264	−	1.40635i	−0.0216344	−	0.0449243i
$981$	−31.8116	+	1.03013i	−1.01567	+	0.0328895i
$982$	17.8378	+	22.3679i	0.569226	+	0.713787i
$983$	5.02289	+	44.5794i	0.160205	+	1.42186i	0.774394	+	0.632703i	$0.218055\pi$
$983$	5.02289	+	44.5794i	0.160205	+	1.42186i	−0.614189	+	0.789159i	$0.710517\pi$
$984$	−14.0034	−	21.5056i	−0.446412	−	0.685573i
$985$			7.23315i			0.230467i
$986$	19.1631	−	25.3477i	0.610278	−	0.807234i
$987$	4.40077	+	17.9377i	0.140078	+	0.570963i
$988$	0.530501	−	0.185630i	0.0168775	−	0.00590569i
$989$	−32.9670	+	3.71448i	−1.04829	+	0.118114i
$990$	−10.2846	−	4.54881i	−0.326865	−	0.144571i
$991$	10.6671	−	22.1505i	0.338852	−	0.703633i	−0.660014	−	0.751254i	$-0.729450\pi$
$991$	10.6671	−	22.1505i	0.338852	−	0.703633i	0.998865	+	0.0476206i	$0.0151638\pi$
$992$	−47.2858	+	22.7717i	−1.50133	+	0.723001i
$993$	−12.8100	+	27.7400i	−0.406513	+	0.880303i
$994$	19.7133	−	31.3735i	0.625267	−	0.995107i
$995$	4.33053	+	18.9733i	0.137287	+	0.601494i
$996$	−15.9981	+	2.06528i	−0.506920	+	0.0654409i
$997$	−27.1748	−	43.2484i	−0.860634	−	1.36969i	−0.928241	−	0.371979i	$-0.878679\pi$
$997$	−27.1748	−	43.2484i	−0.860634	−	1.36969i	0.0676073	−	0.997712i	$-0.478463\pi$
$998$	25.2378	−	25.2378i	0.798887	−	0.798887i
$999$	−36.9320	+	20.0494i	−1.16848	+	0.634335i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	87.2.k.a.11.2	yes	96
3.2	odd	2	inner	87.2.k.a.11.7	yes	96
29.8	odd	28	inner	87.2.k.a.8.7	yes	96
87.8	even	28	inner	87.2.k.a.8.2	✓	96

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
87.2.k.a.8.2	✓	96	87.8	even	28	inner
87.2.k.a.8.7	yes	96	29.8	odd	28	inner
87.2.k.a.11.2	yes	96	1.1	even	1	trivial
87.2.k.a.11.7	yes	96	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 87 = 3 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	87.k (of order \(28\), degree \(12\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.576259 - 1.64685i) q^{2} +(0.598445 + 1.62538i) q^{3} +(-0.816387 + 0.651047i) q^{4} +(1.59790 + 0.769508i) q^{5} +(2.33190 - 1.92219i) q^{6} +(1.54710 - 1.94000i) q^{7} +(-1.41204 - 0.887242i) q^{8} +(-2.28373 + 1.94540i) q^{9} +(0.346463 - 3.07494i) q^{10} +(-1.02572 + 0.644501i) q^{11} +(-1.54676 - 0.937325i) q^{12} +(-1.08029 - 0.246570i) q^{13} +(-4.08643 - 1.42990i) q^{14} +(-0.294489 + 3.05770i) q^{15} +(-1.11217 + 4.87274i) q^{16} +(-2.39140 - 2.39140i) q^{17} +(4.51981 + 2.63991i) q^{18} +(0.482698 + 0.0543871i) q^{19} +(-1.80549 + 0.412091i) q^{20} +(4.07910 + 1.35364i) q^{21} +(1.65248 + 1.31781i) q^{22} +(3.99989 + 8.30586i) q^{23} +(0.597080 - 2.82606i) q^{24} +(-1.15631 - 1.44997i) q^{25} +(0.216464 + 1.92117i) q^{26} +(-4.52870 - 2.54771i) q^{27} +2.59103i q^{28} +(-5.27938 - 1.06215i) q^{29} +(5.20529 - 1.27705i) q^{30} +(-9.19909 + 3.21890i) q^{31} +(5.35125 - 0.602941i) q^{32} +(-1.66139 - 1.28148i) q^{33} +(-2.56022 + 5.31635i) q^{34} +(3.96496 - 1.90942i) q^{35} +(0.597858 - 3.07502i) q^{36} +(4.30274 - 6.84777i) q^{37} +(-0.188592 - 0.826274i) q^{38} +(-0.245726 - 1.90345i) q^{39} +(-1.57355 - 2.50430i) q^{40} +(6.28241 - 6.28241i) q^{41} +(-0.121364 - 7.49772i) q^{42} +(-1.18857 + 3.39673i) q^{43} +(0.417782 - 1.19395i) q^{44} +(-5.14617 + 1.35121i) q^{45} +(11.3736 - 11.3736i) q^{46} +(2.28637 + 3.63873i) q^{47} +(-8.58562 + 1.10836i) q^{48} +(0.187557 + 0.821739i) q^{49} +(-1.72155 + 2.73983i) q^{50} +(2.45581 - 5.31805i) q^{51} +(1.04247 - 0.502026i) q^{52} +(5.08537 - 10.5599i) q^{53} +(-1.58600 + 8.92625i) q^{54} +(-2.13494 + 0.240550i) q^{55} +(-3.90581 + 1.36670i) q^{56} +(0.200469 + 0.817117i) q^{57} +(1.29308 + 9.30643i) q^{58} -2.84288i q^{59} +(-1.75029 - 2.68800i) q^{60} +(0.299240 + 2.65582i) q^{61} +(10.6021 + 13.2946i) q^{62} +(0.240929 + 7.44017i) q^{63} +(0.260480 + 0.540893i) q^{64} +(-1.53646 - 1.22529i) q^{65} +(-1.15302 + 3.47454i) q^{66} +(11.9366 - 2.72445i) q^{67} +(3.50922 + 0.395394i) q^{68} +(-11.1065 + 11.4720i) q^{69} +(-5.42938 - 5.42938i) q^{70} +(-1.90444 + 8.34388i) q^{71} +(4.95075 - 0.720761i) q^{72} +(1.41405 + 0.494798i) q^{73} +(-13.7568 - 3.13989i) q^{74} +(1.66476 - 2.74717i) q^{75} +(-0.429477 + 0.269859i) q^{76} +(-0.336554 + 2.98700i) q^{77} +(-2.99310 + 1.50155i) q^{78} +(1.96273 + 1.23326i) q^{79} +(-5.52674 + 6.93032i) q^{80} +(1.43082 - 8.88554i) q^{81} +(-13.9665 - 6.72591i) q^{82} +(6.97313 - 5.56088i) q^{83} +(-4.21141 + 1.55059i) q^{84} +(-1.98101 - 5.66141i) q^{85} +6.27884 q^{86} +(-1.43302 - 9.21664i) q^{87} +2.02018 q^{88} +(3.09433 + 8.84308i) q^{89} +(5.19077 + 7.69634i) q^{90} +(-2.14967 + 1.71431i) q^{91} +(-8.67297 - 4.17668i) q^{92} +(-10.7371 - 13.0257i) q^{93} +(4.67492 - 5.86216i) q^{94} +(0.729452 + 0.458345i) q^{95} +(4.18244 + 8.33700i) q^{96} +(-0.582251 + 5.16762i) q^{97} +(1.24520 - 0.782413i) q^{98} +(1.08865 - 3.46730i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 96 q - 12 q^{3} - 28 q^{4} - 14 q^{6} - 20 q^{7} - 14 q^{9} - 4 q^{10} - 8 q^{12} - 28 q^{13} - 16 q^{15} - 48 q^{16} - 28 q^{18} - 20 q^{19} + 26 q^{21} - 28 q^{22} + 58 q^{24} - 20 q^{25} + 36 q^{27}+ \cdots + 82 q^{99}+O(q^{100}) \) 96 * q - 12 * q^3 - 28 * q^4 - 14 * q^6 - 20 * q^7 - 14 * q^9 - 4 * q^10 - 8 * q^12 - 28 * q^13 - 16 * q^15 - 48 * q^16 - 28 * q^18 - 20 * q^19 + 26 * q^21 - 28 * q^22 + 58 * q^24 - 20 * q^25 + 36 * q^27 + 96 * q^30 - 32 * q^31 + 28 * q^33 - 28 * q^34 + 22 * q^36 - 4 * q^37 - 40 * q^39 - 48 * q^40 - 14 * q^42 - 32 * q^43 + 42 * q^45 + 120 * q^46 - 20 * q^48 + 4 * q^49 - 14 * q^51 + 72 * q^52 - 30 * q^54 + 148 * q^55 + 112 * q^58 + 20 * q^60 + 12 * q^61 - 14 * q^63 + 224 * q^64 - 32 * q^66 + 28 * q^67 + 10 * q^69 + 52 * q^70 - 44 * q^72 + 16 * q^73 - 144 * q^75 - 100 * q^76 - 102 * q^78 - 60 * q^79 - 146 * q^81 - 108 * q^82 - 64 * q^84 - 104 * q^85 - 70 * q^87 - 312 * q^88 - 96 * q^90 - 112 * q^91 - 70 * q^93 + 56 * q^94 - 168 * q^96 + 32 * q^97 + 82 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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